Border Infrastructure Safety and Congestion Relief Act of 1996 - Authorizes the Secretary of Transportation to make grants to border States (California, Arizona, New Mexico, and Texas) for certain transportation projects necessary to: (1) relieve congestion due to increased traffic resulting from implementation of the North American Free Trade Agreement (NAFTA); or (2) improve enforcement of motor carrier safety laws. Limits the Federal share of the costs of such projects to 80 percent.

Establishes the Border Transportation Infrastructure Fund.

Authorizes appropriations.

Authorizes the Secretary, at the Attorney General's request, to transfer up to $10 million of amounts from the Fund to the Attorney General for construction of transportation infrastructure necessary for law enforcement in border States.

Amends the National Highway System Designation Act of 1995 to authorize appropriations and enter into agreements to make lines of credit available to: (1) border States that have established infrastructure banks to advance transportation infrastructure projects supporting international trade and commerce in the region; and (2) the New Mexico Border Authority.

Authorizes appropriations to provide assistance for freight rail projects in border States that benefit international trade and relieve highways of increased traffic resulting from NAFTA.