Firearm Safety and Buyback Grant Act of 2013 - Amends the Internal Revenue Code to impose upon the seller of any concealable firearm an excise tax equal to 10% of its retail sales price. Exempts sales to federal, state, or local governments. Makes any person who uses a concealable firearm prior to its first retail sale liable for such tax as if such person sold such firearm at retail.
Directs the Attorney General to award grants to states, Indian tribal governments, and local governments for their law enforcement agencies to carry out anti-violence and gun safety campaigns and firearms buyback programs.