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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2006-03-27</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001094572</issuerCik>
        <issuerName>ICOP DIGITAL, INC</issuerName>
        <issuerTradingSymbol>ICOP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000704159</rptOwnerCik>
            <rptOwnerName>PAULSON CAPITAL CORP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>811 SW NAITO PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 200</rptOwnerStreet2>
            <rptOwnerCity>PORTLAND</rptOwnerCity>
            <rptOwnerState>OR</rptOwnerState>
            <rptOwnerZipCode>97204</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>See Footnote (1)</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000898196</rptOwnerCik>
            <rptOwnerName>PAULSON CHESTER L F</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>811 SW NAITO PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 200</rptOwnerStreet2>
            <rptOwnerCity>PORTLAND</rptOwnerCity>
            <rptOwnerState>OR</rptOwnerState>
            <rptOwnerZipCode>97204</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>See Footnote (1)</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000897686</rptOwnerCik>
            <rptOwnerName>PAULSON JACQUELINE M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>811 SW NAITO PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 200</rptOwnerStreet2>
            <rptOwnerCity>PORTLAND</rptOwnerCity>
            <rptOwnerState>OR</rptOwnerState>
            <rptOwnerZipCode>97204</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>See Footnote (1)</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2007-03-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>925</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>6.80</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>611375</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2007-03-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5100</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>6.75</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>606275</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2007-03-28</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>13975</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>6.75</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>592300</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrants</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>6.1875</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2007-03-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>7200</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.75</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2005-07-08</value>
            </exerciseDate>
            <expirationDate>
                <value>2010-07-08</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>7200</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>907764</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrants</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>6.1875</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2007-03-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>880</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.75</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2005-07-08</value>
            </exerciseDate>
            <expirationDate>
                <value>2010-07-08</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>880</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>906884</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Form filed by more than one reporting person.  In addition to Paulson Capital Corp. (&quot;PLCC&quot;), the following are reporting parties:  Chester L.F. Paulson, Jacqueline M. Paulson, Paulson Family LLC (&quot;LLC&quot;) and Paulson Investment Company, Inc. (&quot;PICI&quot;).  These reporting parties collectively own over 10%.  The address for each of the reporting parties is the same as that provided for PLCC.  PICI is a registered broker-dealer and a wholly owned subsidiary of PLCC.  Mr. and Mrs. Paulson are controlling managers of the LLC, which is a controlling shareholder of PLCC, which is the parent company of PICI.  Mr. and Mrs. Paulson and the LLC expressly disclaim any beneficial ownership of securities held in the name of PLCC and PICI.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Harry L. Striplin, Attorney-in-Fact for Chester L.F. Paulson</signatureName>
        <signatureDate>2007-03-28</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Harry L. Striplin, Authorized Agent for Paulson Capital Corp.</signatureName>
        <signatureDate>2007-03-28</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Harry L. Striplin, Authorized Agent for Paulson Investment Co., Inc.</signatureName>
        <signatureDate>2007-03-28</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Harry L. Striplin, Authorized Agent for Paulson Family LLC</signatureName>
        <signatureDate>2007-03-28</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Harry L. Striplin, Attorney-in-Fact for Jacqueline M. Paulson</signatureName>
        <signatureDate>2007-03-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
