No, you are not eligible for the Child Tax Credit if you only have an Individual Taxpayer Identification Number (ITIN). To claim the Child Tax Credit, the qualifying child must have a Social Security Number (SSN) that is valid for employment in the United States. This requirement is specified in the Internal Revenue Code and IRS guidelines.
Sources:
Publication 501 (2023)
§ 24. Child tax credit
Publication 1915 (2/2021)
IRM Part 4. Examining Process. Chapter 19. Liability Determination. Section 14. Refundable Credits Strategy
Publication 1915 (6/2023)