You are not eligible for the Earned Income Credit if you (or your spouse if filing a joint return) have an individual taxpayer identification number (ITIN), instead of a valid social security number.
A child with an ITIN or ATIN (Adoption Taxpayer Identification Number) is not a qualifying child for Earned Income Credit. The child must have a valid social security number.
ITINs are issued by the Internal Revenue Service to noncitizens that cannot get a social security number.
ATINs are issued for the child to adopting parents who cannot get a social security number for the child until the adoption is final.
Per IRS Publication 596 Earned Income Credit (EIC), on page 5:
Other taxpayer identification number. You can’t get the EIC if, instead of an SSN, you (or your spouse, if filing a joint return) have an individual taxpayer identification number (ITIN). ITINs are issued by the Internal Revenue Service to noncitizens who can’t get an SSN.
On page 12:
CAUTION! Social security number. Your qualifying child must have a valid social security number (SSN) on or before the due date of your 2020 return (including extensions), unless the child was born and died in 2020 and you attach to your return a copy of the child's birth certificate, death certificate, or hospital records showing a live birth. You can’t claim the EIC on the basis of a qualifying child if:
If you have more than one qualifying child and only one has a valid SSN, you can use only that child to claim the EIC. For more information about SSNs, see Rule 2.
Note that any link in the information above is updated each year automatically and will take you to the most recent version of the document at the time it is accessed.