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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

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

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001427925</issuerCik>
        <issuerName>ACELRX PHARMACEUTICALS INC</issuerName>
        <issuerTradingSymbol>ACRX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001628970</rptOwnerCik>
            <rptOwnerName>ASADORIAN RAFFI</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ACELRX PHARMACEUTICALS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>25821 INDUSTRIAL BLVD., SUITE 400</rptOwnerStreet2>
            <rptOwnerCity>HAYWARD</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94545</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Financial Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-03-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>7923</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.4068</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>364205</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares surrendered to the Issuer by the Reporting Person to pay required tax withholdings due to the vesting of RSUs.</footnote>
        <footnote id="F2">Includes previously reported shares of common stock underlying RSUs granted to the Reporting Person, which are subject to certain vesting conditions.</footnote>
        <footnote id="F3">Balance includes non-reportable acquisition of 4,040 shares of Common Stock through the Company's Employee Stock Purchase Plan.</footnote>
        <footnote id="F4">On February 14, 2022, the reporting person filed a Form 4 which inadvertently under-reported his holdings in the Issuer by 8 shares. In addition to reporting the current transactions, this Form 4 serves to correct the reporting person's holdings in the Issuer.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Martha Adler, Attorney-In-Fact</signatureName>
        <signatureDate>2022-03-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
