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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-04-14</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000096021</issuerCik>
        <issuerName>SYSCO CORP</issuerName>
        <issuerTradingSymbol>SYY</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001839288</rptOwnerCik>
            <rptOwnerName>Orting Jorgensen Tim</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1390 ENCLAVE PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77077</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2021-04-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>27218</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27218</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Restricted stock units granted by the Compensation and Leadership Development Committee of the Company's Board of Directors pursuant to the 2018 Omnibus Incentive Plan.  This award of restricted stock units was made in connection with the reporting person's hiring as the Company's Executive Vice President and President, Foodservice Operations, International.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Gerald W. Clanton, Attorney-in-fact</signatureName>
        <signatureDate>2021-04-16</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2021-04-14
0
0000096021
SYSCO CORP
SYY
0001839288
Orting Jorgensen Tim
1390 ENCLAVE PARKWAY
HOUSTON
TX
77077
0
1
0
0
EVP
Common Stock
2021-04-14
4
A
0
27218
0
A
27218
D
Restricted stock units granted by the Compensation and Leadership Development Committee of the Company's Board of Directors pursuant to the 2018 Omnibus Incentive Plan.  This award of restricted stock units was made in connection with the reporting person's hiring as the Company's Executive Vice President and President, Foodservice Operations, International.
Gerald W. Clanton, Attorney-in-fact
2021-04-16