Yes. The child tax credit can only be claimed by the parent claiming an the exemption for the child.

 

You can claim both the child tax credit and the child and dependent care credit on the same return if you qualify for both credits.

• If you qualify for one or both credits, you can claim the credits on Form 1040 (PDF), U.S. Individual Income Tax Return, or Form 1040A (PDF), U.S. Individual Income Tax Return. If you are claiming the dependent care credit, you must complete Form 2441.
• Refer to "Child tax credit" in the index to the Form 1040 Instructions or the Form 1040A Instructions.  The instructions will explain who qualifies for the child tax credit, and how to calculate it.
  
• The Form 2441 Instructions will explain who qualifies for the dependent care credit, and how to calculate it.  

Yes, you can claim the child tax credit for a child with an ITIN (individual tax identification number) if you otherwise qualify.

For information on an ITIN, refer to the section on Social Security Numbers for Dependents in Publication 501, Exemptions, Standard Deduction, and Filing Information.