Trafficking Reduction and Criminal Enforcement (TRACE) Act - Directs the Attorney General to promulgate regulations that require each firearm manufactured in the United States to be marked with a serial number that is located inside the firearm's receiver or that is visible only in infrared light, in addition to the serial number mark otherwise required.

Amends the federal criminal code to: (1) prohibit national instant criminal background check system records about a prospective firearm transferee from being destroyed until after 180 days after the system assigns and provides a firearms licensee with a unique identification number for the transfer, and (2) repeal provisions prohibiting appropriated funds from being used for any system that does not require the destruction of any identifying information submitted for a transferee within 24 hours after the system advises a licensee that the transferee's receipt of a firearm is not prohibited.

Requires each licensed firearms dealer to conduct a physical check of its firearms business inventory. Amends the Consolidated and Further Continuing Appropriations Act, 2012, to repeal prohibitions against using appropriated funds to: (1) promulgate or implement any rule requiring a physical inventory of any firearms business; or (2) disclose contents of the Firearms Trace System database maintained by the National Trace Center of the Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF) or any information required to be kept by firearms licensees except as specified in that Act.