This paper discusses the design of an adaptive command-filtered backstepping flight control law with uncertain parameters for a quadrotor unmanned aerial vehicle (UAV). The control law is tasked with tracking reference trajectories with a constrained velocity, attitude, and attitude rate. Thruster misalignment is included in the formulation of the quadrotor dynamics. Online parameter update laws are used to compensate for the uncertain parameters, namely mass, inertia, actuator gain, and thruster misalignment. Command filters are used to implement the vehicle's actuator and state constraints. Stability of the control law with parameter update laws during periods of saturation is guaranteed by using a modified tracking error in the Lyapunov function, in which the effect of the saturation is smoothed into the other internal control steps. The controller and its performance are evaluated using a non-linear, six-degree-of-freedom dynamic model of a quadrotor UAV in simulations. The results show that the proposed control law enhances the tracking performance by controlling internal states even with parameter uncertainties and thruster misalignment errors.