Respecting States' Rights and Concealed Carry Reciprocity Act of 2013 - Amends the federal criminal code to authorize a person who is not prohibited from possessing, transporting, shipping, or receiving a firearm under federal law, who is entitled and not prohibited from carrying a concealed firearm in his or her state of residence or who is carrying a valid state license or permit to carry a concealed weapon, and who is carrying a government-issued photographic identification document, to carry a concealed handgun (which has been shipped or transported in interstate or foreign commerce, other than a machine gun or destructive device) in any state in accordance with the restrictions of that state.

Provides that in a state that allows the issuing authority for licenses or permits to carry concealed firearms to impose restrictions on the carrying of firearms by individual license or permit holders, an individual carrying a concealed handgun under this Act shall be permitted to carry it according to the same terms authorized by an unrestricted license or permit issued by such state.