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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-09-22</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001600420</rptOwnerCik>
            <rptOwnerName>COLUMN GROUP II, LP</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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001645333</rptOwnerCik>
            <rptOwnerName>Column Group II GP, LP</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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>General Partner</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001707230</rptOwnerCik>
            <rptOwnerName>PONOI CAPITAL, LP</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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001720702</rptOwnerCik>
            <rptOwnerName>Ponoi Management, LLC</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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>General Partner</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001732601</rptOwnerCik>
            <rptOwnerName>Ponoi Capital II, LP</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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001746488</rptOwnerCik>
            <rptOwnerName>Ponoi II Management, LLC</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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>General Partner</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001783952</rptOwnerCik>
            <rptOwnerName>Column Group II Management, LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1700 OWENS STREET, SUITE 500</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94158</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001614186</rptOwnerCik>
            <rptOwnerName>Kutzkey Tim</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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Managing Partner</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001182464</rptOwnerCik>
            <rptOwnerName>GOEDDEL DAVID V</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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Managing Partner</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-09-22</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>608000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>30.85</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3835679</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1599417</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>145401</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>50000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F4"/>
                </directOrIndirectOwnership>
            </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 managing partners of TCG II GP are David Goeddel and Peter Svennilson. The managing partners of TCG II GP may be deemed to have voting and investment power with respect to such shares. TCG II GP and each individual managing partner disclaims beneficial ownership of these shares, except to the extent of their respective 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 managing partners of Ponoi LLC are David Goeddel, Peter Svennilson and Tim Kutzkey. The managing partners of Ponoi LLC may be deemed to have voting and investment power with respect to such shares. Each individual managing partner 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 managing partners of Ponoi II LLC are David Goeddel, Peter Svennilson and Tim Kutzkey. The managing partners of Ponoi II LLC may be deemed to have voting and investment power with respect to such shares. Each individual managing partner 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;). Under the partnership agreement of TCG II LP, TCGM II LP is deemed to hold the securities for the economic benefit of TCG II LP. TCG II LP may be deemed to have an indirect pecuniary interest in the securities. The managing partners of TCGM II LP are David Goeddel and Peter Svennilson. The managing partners of TCGM II LP may be deemed to have voting and investment power with respect to such securities. TCGM II LP, TCG II LP and each individual managing partner disclaims beneficial ownership of these securities, except to the extent of their pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jennifer J. Carlson, Attorney-in-fact</signatureName>
        <signatureDate>2020-09-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
