Redistricting Reform Act of 2013 - Prohibits a state that has been redistricted after an apportionment from being redistricted again until after the next apportionment of Representatives, unless the state is ordered by a court to conduct such a subsequent redistricting in order to: (1) comply with the U.S. Constitution, or (2) enforce the Voting Rights Act of 1965.

Requires such redistricting to be conducted according to: (1) a plan developed by the independent redistricting commission established in the state; or (2) if such plan is not enacted into law, the redistricting plan selected by the state's highest court or developed by a U.S. district court.

Provides for: (1) establishment by each state of an independent redistricting commission; (2) development by such commission of a redistricting plan; (3) submission of the plan to, and consideration and enactment of a plan by, the state legislature; (4) selection of a plan by the state's highest court or development of a plan by the U.S. district court, under specified conditions; (5) special rules for redistricting conducted under a federal court order; (6) Election Assistance Commission payments to states for carrying out redistricting; (7) civil enforcement to carry out this Act; and (8) the right of civil action for a person who is aggrieved by a violation of this Act.