Yes, Airbus does use Rolls Royce engines.
The Rolls-Royce Trent 900 engine, for example, is specifically designed to power the Airbus A380 aircraft. This engine competes with the Engine Alliance GP7000 in the A380 market. This indicates a direct relationship between Airbus and Rolls-Royce, where Rolls-Royce provides engines for Airbus aircraft.
