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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-11-12</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001807427</issuerCik>
        <issuerName>Owl Rock Capital Corp III</issuerName>
        <issuerTradingSymbol>NONE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001676100</rptOwnerCik>
            <rptOwnerName>Packer Craig</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O OWL ROCK CAPITAL CORPORATION III</rptOwnerStreet1>
            <rptOwnerStreet2>399 PARK AVENUE, 38TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>CEO and President</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2021-11-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>839401</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>15.15</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3718523</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Reflects the shares held by Owl Rock Feeder FIC BDC III LLC. Mr. Packer disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein, and this report shall not be deemed an admission for purposes of Section 16 or for any other purpose.</footnote>
    </footnotes>

    <remarks>(2) Neena Reddy is signing on behalf of Mr. Packer pursuant to a power of attorney dated February 19, 2020, which was previously filed with the Securities and Exchange Commission as an exhibit to the Form 3 Mr. Packer filed on August 4, 2020.</remarks>

    <ownerSignature>
        <signatureName>/s/ Neena Reddy on behalf of Craig Packer(2)</signatureName>
        <signatureDate>2021-11-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
