Fair Allocation of Internal Revenue Credit for Renewable Electricity Distribution by Indian Tribes Act of 2013 or the FAIR CREDIT Act of 2013 - Amends the Internal Revenue Code, for purposes of the renewable electricity production tax credit, to allow an Indian tribe that has an ownership interest in the gross sales from a facility that uses a renewable energy resource to produce electricity to assign to any other person who has such an ownership interest any portion of the production from the facility that would, but for this Act, be allocated to such tribe.