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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-03-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001439404</issuerCik>
        <issuerName>ZYNGA INC</issuerName>
        <issuerTradingSymbol>ZNGA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001337679</rptOwnerCik>
            <rptOwnerName>GIBEAU FRANK D</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ZYNGA INC.</rptOwnerStreet1>
            <rptOwnerStreet2>699 8TH STREET</rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94103</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
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            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-03-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-03-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <footnoteId id="F2"/>
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                <value></value>
            </transactionTimeliness>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
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            </postTransactionAmounts>
            <ownershipNature>
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                </directOrIndirectOwnership>
            </ownershipNature>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
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                </transactionShares>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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            <deemedExecutionDate></deemedExecutionDate>
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            <transactionTimeliness>
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            </transactionTimeliness>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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            </transactionCoding>
            <transactionTimeliness>
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            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                </sharesOwnedFollowingTransaction>
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        <nonDerivativeTransaction>
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                <value>Class A Common Stock</value>
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            <transactionDate>
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            <deemedExecutionDate></deemedExecutionDate>
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                <transactionPricePerShare>
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        <nonDerivativeTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trust</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
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                <transactionPricePerShare>
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            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>62969</value>
                    <footnoteId id="F10"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F11"/>
            </exerciseDate>
            <expirationDate>
                <value>2028-03-15</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>62969</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>188904</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each restricted stock unit represents a contingent right to receive 1 share of the Issuer's Class A Common Stock upon vest.</footnote>
        <footnote id="F2">Represents shares sold to satisfy tax withholding obligations in connection with the vesting of the restricted stock units described in Table II.</footnote>
        <footnote id="F3">Represents shares withheld to satisfy tax withholding obligations in connection with the vesting of the restricted stock units described in Table II.</footnote>
        <footnote id="F4">Shares held directly by Frank Donald Gibeau Trust U/A DTD 12/13/2019. Mr. Gibeau serves as trustee and holds voting and dispositive power with respect to these shares.</footnote>
        <footnote id="F5">25% of the shares subject to the award vested on March 15, 2020, and 6.25% of the shares subject to the award vest quarterly thereafter, generally subject to continued service to the Issuer through each vesting date.</footnote>
        <footnote id="F6">25% of the shares subject to the award will vest on March 15, 2021, and 6.25% of the shares subject to the award vest quarterly thereafter for a
period of four years after the commencement date, generally subject to continued service to the Issuer through each vesting date.</footnote>
        <footnote id="F7">5% of the shares subject to the award will vest on June 15, 2021, and 5% of the shares subject to the award vest quarterly thereafter, generally subject to continued service to the Issuer through each vesting date.</footnote>
        <footnote id="F8">Each PSU represents a contingent right to receive a share of the Issuer's Class A common stock based upon the achievement of a specified
financial metric (the Issuer's annual operating cash flow). Once the number of earned shares (if any) subject to the PSUs have been
determined, 25% of the earned shares will vest on March 15, 2021, and 6.25% of the earned shares will vest quarterly thereafter, generally
subject to the reporting person's continued service to the Issuer through each vesting date.</footnote>
        <footnote id="F9">25% of the shares subject to the award vested on March 15, 2022, and 6.25% of the shares subject to the award vest quarterly thereafter, generally subject to continued service to the Issuer through each vesting date</footnote>
        <footnote id="F10">Amounts represent the actual number of earned shares subject to the performance stock award, as determined by the Issuer's board of directors.</footnote>
        <footnote id="F11">Each PSU represents a contingent right to receive a share of the Issuer's Class A common stock based upon the achievement of a specified financial metric (the Issuer's annual operating cash flow). Once the number of earned shares (if any) subject to the PSUs have been determined, 25% of the earned shares will vest on March 15, 2022, and 6.25% of the earned shares will vest quarterly thereafter, generally subject to the reporting person's continued service to the Issuer through each vesting date. The number of shares reported herein is a target number, and the actual number of shares issuable pursuant to the PSU will range from 0-150% of the number of target shares.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Matt Tolland, as attorney-in-fact for Frank D. Gibeau</signatureName>
        <signatureDate>2022-03-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
