Yes, each registered domestic partner may qualify to claim the adoption credit for the amount of the qualified adoption expenses paid for the adoption. However, the partners may not both claim a credit for the same qualified adoption expenses, and the sum of the credit taken by each registered domestic partner may not exceed the total amount paid.
The adoption credit is limited to $12,970 per child in 2013. Thus, if both registered domestic partners paid qualified adoption expenses to adopt the same child, and the total of those expenses exceeds $12,970, the maximum credit available for the adoption is $12,970. The registered domestic partners may allocate this maximum between them in any way they agree, and the amount of credit claimed by one registered domestic partner can exceed the adoption expenses paid by that person, as long as the total credit claimed by both registered domestic partners does not exceed the total amount paid by them.
Sources:
Publication 17 (2023)
Publication 501 (2023)