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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-06-18</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>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>28.27</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-06-18</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>22500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-06-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>22500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>22500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The Option shall vest in a series of three successive equal annual installments over the three-year period measured from the date of grant, subject to the Reporting Person's continuous service through each applicable vesting date.</footnote>
        <footnote id="F2">The Reporting Person is a managing partner of The Column Group II GP, LP, Ponoi Management, LLC and Ponoi II Management, LLC which are the general partners of The Column Group II, LP (&quot;TCG II LP&quot;), Ponoi Capital, LP (&quot;Ponoi LP&quot;) and Ponoi Capital II, LP (&quot;Ponoi II LP&quot;), respectively. Under the partnership agreements of TCG II LP, Ponoi LP and Ponoi II LP (collectively, the &quot;Funds&quot;), the Reporting Person is deemed to hold the Option for the economic benefit of the Funds. The Funds and their respective general partners may be deemed indirect beneficial owners of the Option and the Reporting Person may be deemed the indirect beneficial owner of the Option through his indirect interest in the Funds. The Reporting Person disclaims beneficial ownership of the Option except to the extent of his pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jennifer J. Carlson, Attorney-in-Fact</signatureName>
        <signatureDate>2020-06-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
