To be eligible for the Child Tax Credit the child must have a Social Security number. If the child does not have a SSN but some other identification such as an ITIN the child is only eligible for the Other Dependent credit of $500.
Go to this IRS website for the Schedule 8812, Credits for Qualifying Children and Other Dependents instructions on page 1 - https://www.irs.gov/pub/irs-pdf/i1040s8.pdf
