Universal Screening of Air Cargo Act - Requires the screening of all cargo that is to be transported in passenger aircraft operated by domestic and foreign air carriers. Requires the Under Secretary of Border and Transportation Security of the Department of Homeland Security to: (1) develop a plan to implement such screening; (2) establish a fee schedule for shippers to cover the costs of screening; (3) monitor and evaluate new cargo screening technologies; (4) establish a system for the regular inspection of shipping facilities for shipments of air cargo; and (5) establish a training and evaluation program for air cargo handlers.