This paper presents the development of a robust adaptive controller for the dynamics of a quadrotor unmanned aerial vehicle (UAV) in the presence of linear-in-the-parameter uncertainties and bounded exogenous disturbances. The controller is designed to asymptotically track a desired position and yaw angle trajectory via a modular adaptive update law and a robust integral sign of the error (RISE) feedback term. A Lyapunov-based stability analysis is used to prove asymptotic tracking of the desired states and to ensure all closed-loop signals remain bounded.