This paper addresses the problem of designing and experimentally validating a controller for steering a quadrotor vehicle along a trajectory, while rejecting constant force disturbances. The proposed solution consists of a nonlinear adaptive state feedback controller that asymptotically stabilizes the closed-loop system in the presence of force disturbances. We consider two methods of angular actuation for the quadrotor, angular velocity and torque, and ensure that the actuation does not grow unbounded as a function of the position error. The constant force disturbance is estimated through the use of a sufficiently smooth projector operator. A prototyping and testing architecture, developed to streamline the implementation and the tuning of the controller, is also described. Experimental results are presented to demonstrate the performance and robustness of the proposed controller.