Do I qualify for an adoption tax credit if adopting a child out of foster care and no out of pocket expenses are paid by me?

You qualify for the credit if you adopted an eligible U.S. child with special needs. (In this case, you may be able to take the credit even if you didn't pay any qualified adoption expenses.)

The definition of a special needs child is not what we typically think of as special needs. 

For more information see IRS Instructions for Form 8839.