Uniting American Families Act of 2013 - Amends the Immigration and Nationality Act to include a "permanent partner" within the scope of such Act. Defines a "permanent partner" as an individual 18 or older who: (1) is in a committed, intimate relationship with another individual 18 or older in which both individuals intend a lifelong commitment; (2) is financially interdependent with the other individual; (3) is not married to, or in a permanent partnership with, anyone other than the individual; (4) is unable to contract with the other individual a marriage cognizable under this Act; and (5) is not a first, second, or third degree blood relation of the other individual.

Defines: (1) "permanent partnership" as the relationship existing between two permanent partners, and (2) "alien permanent partner" as the individual in a permanent partnership who is being sponsored for a visa.