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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-08-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001673772</issuerCik>
        <issuerName>RAPT Therapeutics, Inc.</issuerName>
        <issuerTradingSymbol>RAPT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001606074</rptOwnerCik>
            <rptOwnerName>Svennilson Peter</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1700 OWENS STREET</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 500</rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94158</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-08-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>538654</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>22.75</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4443679</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <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="F2"/>
                </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="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>50000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The securities are directly held by The Column Group II, LP (&quot;TCG II LP&quot;) and indirectly held by The Column Group II GP, LP (&quot;TCG II GP&quot;), the general partner of TCG II LP. The Reporting Person is one of the managing partners of TCG II GP. The managing partners of TCG II GP may be deemed to have voting and investment power with respect to such shares. The Reporting Person disclaims beneficial ownership of these shares, except to the extent of his pecuniary interest in such shares.</footnote>
        <footnote id="F2">The securities are directly held by Ponoi Capital, LP (&quot;Ponoi LP&quot;) and indirectly held by Ponoi Management, LLC (&quot;Ponoi LLC&quot;), the general partner of Ponoi LP. The Reporting Person is one of the managing partners of Ponoi LLC.  The managing partners of Ponoi LLC may be deemed to have voting and investment power with respect to such shares. The Reporting Person disclaims beneficial ownership of these shares, except to the extent of his pecuniary interest in such shares.</footnote>
        <footnote id="F3">The securities are directly held by Ponoi Capital II, LP (&quot;Ponoi II LP&quot;) and indirectly held by Ponoi II Management, LLC (&quot;Ponoi II LLC&quot;), the general partner of Ponoi II LP. The Reporting Person is one of the managing partners of Ponoi II LLC. The managing partners of Ponoi II LLC may be deemed to have voting and investment power with respect to such shares. The Reporting Person disclaims beneficial ownership of these shares, except to the extent of his pecuniary interest in such shares.</footnote>
        <footnote id="F4">The securities are directly held by The Column Group II Management, LP (&quot;TCGM II LP&quot;). The Reporting Person is one of the managing partners of TCGM II LP. The managing partners of TCGM II LP may be deemed to have voting and investment power with respect to such shares. The Reporting Person disclaims beneficial ownership of these shares, except to the extent of his pecuniary interest in such shares.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jennifer J. Carlson, Attorney-in-Fact</signatureName>
        <signatureDate>2020-08-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
