My wife and I had a failed adoption in 2014. We paid all adoption expenses in 2014 through an adoption agency. The baby was born in August 2014 and after 2 month the birth father was granted custody in family court. Will we be able to take the adoption credit when we file our 2014 taxes?

Yes as it is a U.S. adoption and you had qualified adoption expenses. It is treated as a non-finalized adoption, and you must wait one year after you incur the expenses. So, since you had expenses for an adoption in 2014 but the adoption has failed, you claim them with your 2015 taxes, typically filed in early 2016; so, you may treat failed adoption expenses the same way for federal income tax credit purposes that you would treat adoption expenses for an adoption that was not finalized prior to the end of current tax year.