Birthright Citizenship Act of 2013 - Amends the Immigration and Nationality Act to consider a person born in the United States "subject to the jurisdiction" of the United States for citizenship at birth purposes if the person is born in the United States of parents, one of whom is: (1) a U.S. citizen or national, (2) a lawful permanent resident alien whose residence is in the United States, or (3) an alien performing active service in the U.S. Armed Forces.