Gun Trafficking Prevention Act of 2013 - Amends the federal criminal code to prohibit any person, in or affecting interstate commerce: (1) from purchasing, attempting to purchase, or transferring a firearm, with intent to deliver the firearm to another person who the transferor knows or has reasonable cause to believe is prohibited from possessing a firearm; (2) in purchasing, attempting to purchase, or transferring a firearm, from intentionally providing false or misleading material information on a Bureau of Alcohol, Tobacco, Firearms, and Explosives (ATF) firearms transaction record form; or (3) knowingly directing, promoting, or facilitating such a violation. Authorizes an enhanced penalty for the organization or supervision of such conduct.

Makes exceptions for a firearm that is lawfully acquired: (1) to be given to another person not prohibited from possessing it under federal or state law as a gift; or (2) by a court-appointed trustee, receiver, or conservator on behalf of an estate or creditor, to carry out a bequest, or in an acquisition by intestate succession.

Directs the U.S. Sentencing Commission to review and, if appropriate, amend the federal sentencing guidelines and policy statements applicable to persons convicted of offenses under this Act.