It gets a little tricky. AA inherited a large number of A319/320/321 aircraft when it merged with US Airways in 2013. US Airways, in turn, got many of these planes from its 2005 merger with America West Airlines, plus it was in the process of taking deliveries of the A320s it ordered on its own. America West got its first two A320 aircraft in September of 1990 and gradually replaced its fleet of Boeing 737-200/300s. US Airways got its first A320 in January 1999, they replaced the Boeing 737-300/400s and the A321s replaced the Boeing 757.
American Airlines not only kept most of the A319/320/321 it got from the merger, but took over the outstanding orders for the aircraft. At the time American also had large orders for the Boeing 737-800 and later ordered the 737-MAX8, which it plans to operate alongside the Airbuses. The large fleet of A319s allowed American to retire its MD-80s, while the A321s are replacing the Boeing 757s. The newly delivered winglet-equipped (Airbus calls them sharklets) A321s also replaced the Boeing 767-200s on the New York to Los Angeles and San Francisco service.