<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-09-14</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
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        <issuerName>RAPT Therapeutics, Inc.</issuerName>
        <issuerTradingSymbol>RAPT</issuerTradingSymbol>
    </issuer>

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            <rptOwnerCik>0001600420</rptOwnerCik>
            <rptOwnerName>COLUMN GROUP II, LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1 LETTERMAN DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2>BUILDING D, SUITE DM-900</rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94129</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
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    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
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            <rptOwnerName>Column Group II GP, LP</rptOwnerName>
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            <rptOwnerStreet1>1 LETTERMAN DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2>BUILDING D, SUITE DM-900</rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94129</rptOwnerZipCode>
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    </reportingOwner>

    <reportingOwner>
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            <rptOwnerName>PONOI CAPITAL, LP</rptOwnerName>
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        <reportingOwnerAddress>
            <rptOwnerStreet1>1 LETTERMAN DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2>BUILDING D, SUITE DM-900</rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94129</rptOwnerZipCode>
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    <reportingOwner>
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            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
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    <reportingOwner>
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            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94129</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
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    <reportingOwner>
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            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94129</rptOwnerZipCode>
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    <reportingOwner>
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            <rptOwnerCik>0001614186</rptOwnerCik>
            <rptOwnerName>Kutzkey Tim</rptOwnerName>
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            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
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            <rptOwnerStateDescription></rptOwnerStateDescription>
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    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
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            <rptOwnerName>GOEDDEL DAVID V</rptOwnerName>
        </reportingOwnerId>
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            <rptOwnerStreet2>BUILDING D, SUITE DM-900</rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94129</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
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    <reportingOwner>
        <reportingOwnerId>
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            <rptOwnerName>Svennilson Peter</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
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            <rptOwnerStreet2>BUILDING D, SUITE DM-900</rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94129</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
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    <reportingOwner>
        <reportingOwnerId>
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            <rptOwnerName>Column Group LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
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            <rptOwnerStreet2>BUILDING D, SUITE DM-900</rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94129</rptOwnerZipCode>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2021-09-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>1</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4720</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>37.7028</value>
                    <footnoteId id="F16"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1402008</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F17"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>163</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F18"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1599417</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F19"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>145401</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F20"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The price reported in Column 4 is a weighted average price. These securities were sold in multiple transactions at prices ranging from $35.15 to $36.09, inclusive. Peter Svennilson undertakes to provide to the Issuer, any security holder of the Issuer or the staff of the Securities Exchange Commission, upon request, full information regarding the number of securities sold at each separate price within the ranges set forth in this footnote (1) to this Form 4.</footnote>
        <footnote id="F2">These securities are directly held by Peter Svennilson.</footnote>
        <footnote id="F3">The price reported in Column 4 is a weighted average price. These securities were sold in multiple transactions at prices ranging from $36.165 to $37.11, inclusive. Peter Svennilson undertakes to provide to the Issuer, any security holder of the Issuer or the staff of the Securities Exchange Commission, upon request, full information regarding the number of securities sold at each separate price within the ranges set forth in this footnote (3) to this Form 4.</footnote>
        <footnote id="F4">The price reported in Column 4 is a weighted average price. These securities were sold in multiple transactions at prices ranging from $37.18 to $37.50, inclusive. Peter Svennilson undertakes to provide to the Issuer, any security holder of the Issuer or the staff of the Securities Exchange Commission, upon request, full information regarding the number of securities sold at each separate price within the ranges set forth in this footnote (4) to this Form 4.</footnote>
        <footnote id="F5">The price reported in Column 4 is a weighted average price. These securities were sold in multiple transactions at prices ranging from $35.26 to $36.25, inclusive. David Goeddel undertakes to provide to the Issuer, any security holder of the Issuer or the staff of the Securities Exchange Commission, upon request, full information regarding the number of securities sold at each separate price within the ranges set forth in this footnote (5) to this Form 4.</footnote>
        <footnote id="F6">These securities are directly held by David Goeddel.</footnote>
        <footnote id="F7">The price reported in Column 4 is a weighted average price. These securities were sold in multiple transactions at prices ranging from $36.26 to $37.255, inclusive. David Goeddel undertakes to provide to the Issuer, any security holder of the Issuer or the staff of the Securities Exchange Commission, upon request, full information regarding the number of securities sold at each separate price within the ranges set forth in this footnote (7) to this Form 4.</footnote>
        <footnote id="F8">The price reported in Column 4 is a weighted average price. These securities were sold in multiple transactions at prices ranging from $37.26 to $37.465, inclusive. David Goeddel undertakes to provide to the Issuer, any security holder of the Issuer or the staff of the Securities Exchange Commission, upon request, full information regarding the number of securities sold at each separate price within the ranges set forth in this footnote (8) to this Form 4.</footnote>
        <footnote id="F9">The price reported in Column 4 is a weighted average price. These securities were sold in multiple transactions at prices ranging from $35.26 to $36.25, inclusive. Tim Kutzkey undertakes to provide to the Issuer, any security holder of the Issuer or the staff of the Securities Exchange Commission, upon request, full information regarding the number of securities sold at each separate price within the ranges set forth in this footnote (9) to this Form 4.</footnote>
        <footnote id="F10">These securities are directly held by Tim Kutzkey.</footnote>
        <footnote id="F11">The price reported in Column 4 is a weighted average price. These securities were sold in multiple transactions at prices ranging from $36.27 to $37.26, inclusive. Tim Kutzkey undertakes to provide to the Issuer, any security holder of the Issuer or the staff of the Securities Exchange Commission, upon request, full information regarding the number of securities sold at each separate price within the ranges set forth in this footnote (11) to this Form 4.</footnote>
        <footnote id="F12">The price reported in Column 4 is a weighted average price. These securities were sold in multiple transactions at prices ranging from $37.27 to $37.39, inclusive. Tim Kutzkey undertakes to provide to the Issuer, any security holder of the Issuer or the staff of the Securities Exchange Commission, upon request, full information regarding the number of securities sold at each separate price within the ranges set forth in this footnote (12) to this Form 4.</footnote>
        <footnote id="F13">The price reported in Column 4 is a weighted average price. These securities were sold in multiple transactions at prices ranging from $36.53 to $37.51, inclusive. Peter Svennilson undertakes to provide to the Issuer, any security holder of the Issuer or the staff of the Securities Exchange Commission, upon request, full information regarding the number of securities sold at each separate price within the ranges set forth in this footnote (13) to this Form 4.</footnote>
        <footnote id="F14">The price reported in Column 4 is a weighted average price. These securities were sold in multiple transactions at prices ranging from $37.53 to $38.06, inclusive. Peter Svennilson undertakes to provide to the Issuer, any security holder of the Issuer or the staff of the Securities Exchange Commission, upon request, full information regarding the number of securities sold at each separate price within the ranges set forth in this footnote (14) to this Form 4.</footnote>
        <footnote id="F15">The price reported in Column 4 is a weighted average price. These securities were sold in multiple transactions at prices ranging from $36.53 to $37.52, inclusive. David Goeddel undertakes to provide to the Issuer, any security holder of the Issuer or the staff of the Securities Exchange Commission, upon request, full information regarding the number of securities sold at each separate price within the ranges set forth in this footnote (15) to this Form 4.</footnote>
        <footnote id="F16">The price reported in Column 4 is a weighted average price. These securities were sold in multiple transactions at prices ranging from $37.57 to $38.06, inclusive. David Goeddel undertakes to provide to the Issuer, any security holder of the Issuer or the staff of the Securities Exchange Commission, upon request, full information regarding the number of securities sold at each separate price within the ranges set forth in this footnote (16) to this Form 4.</footnote>
        <footnote id="F17">The securities are directly held by The Column Group II, LP (&quot;TCG II LP&quot;). The Column Group II GP, LP (&quot;TCG II GP&quot;) is the general partner of TCG II LP and may be deemed to have voting, investment and dispositive power with respect to these securities. The managing partners of TCG II GP are David Goeddel and Peter Svennilson (collectively, the &quot;TCG II GP Managing Partners&quot;). The TCG II GP Managing Partners may be deemed to share voting and investment power with respect to such shares. TCG II GP and each of the TCG II GP Managing Partners disclaim beneficial ownership of these shares, except to the extent of their respective pecuniary interest in such shares.</footnote>
        <footnote id="F18">The securities are directly held The Column Group LLC (&quot;TCG LLC&quot;). The managing members of TCG LLC are the TCG II GP Managing Partners and Tim Kutzkey (collectively, the &quot;Ponoi Managing Partners&quot;). The Ponoi Managing Partners may be deemed to share voting and investment power with respect to such shares. Each of the Ponoi Managing Partners disclaims beneficial ownership of these shares, except to the extent of their respective pecuniary interest in such shares.</footnote>
        <footnote id="F19">The securities are directly held by Ponoi Capital, LP (&quot;Ponoi LP&quot;). Ponoi Management, LLC (&quot;Ponoi LLC&quot;) is the general partner of Ponoi LP and may be deemed to have voting, investment and dispositive power with respect to these securities. The managing partners of Ponoi LLC are the Ponoi Managing Partners. The Ponoi Managing Partners may be deemed to share voting and investment power with respect to such shares. Ponoi LLC and the each of the Ponoi Managing Partners disclaims beneficial ownership of these shares, except to the extent of their respective pecuniary interest in such shares.</footnote>
        <footnote id="F20">The securities are directly held by Ponoi Capital II, LP (&quot;Ponoi II LP&quot;). Ponoi II Management, LLC (&quot;Ponoi II LLC&quot;) is the general partner of Ponoi II LP and may be deemed to have voting, investment and dispositive power with respect to these securities. The managing partners of Ponoi II LLC are the Ponoi Managing Partners. The Ponoi Managing Partners may be deemed to share voting and investment power with respect to such shares. Ponoi II LLC and the each of the Ponoi Managing Partners disclaims beneficial ownership of these shares, except to the extent of their respective pecuniary interest in such shares.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ James Evangelista, as Attorney-in-fact for David Goeddel</signatureName>
        <signatureDate>2021-09-16</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ James Evangelista, as Attorney-in-fact for Peter Svennilson</signatureName>
        <signatureDate>2021-09-16</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ James Evangelista, as Attorney-in-fact for Tim Kutzkey</signatureName>
        <signatureDate>2021-09-16</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ James Evangelista, as Attorney-in-fact for Ponoi Capital II LP</signatureName>
        <signatureDate>2021-09-16</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ James Evangelista, as Attorney-in-fact for Ponoi II Management LLC</signatureName>
        <signatureDate>2021-09-16</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ James Evangelista, as Attorney-in-fact for Ponoi Capital LP</signatureName>
        <signatureDate>2021-09-16</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ James Evangelista, as Attorney-in-fact for Ponoi Management LLC</signatureName>
        <signatureDate>2021-09-16</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ James Evangelista, as Attorney-in-fact for The Column Group II LP</signatureName>
        <signatureDate>2021-09-16</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ James Evangelista, as Attorney-in-fact for The Column Group II GP LP</signatureName>
        <signatureDate>2021-09-16</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ James Evangelista, as Attorney-in-fact for The Column Group LLC</signatureName>
        <signatureDate>2021-09-16</signatureDate>
    </ownerSignature>
</ownershipDocument>
