In this paper, a fuzzy logic-based fault-tolerant attitude control strategy is proposed for the attitude tracking of a quadrotor unmanned aerial vehicle (UAV) subject to actuator faults. The attitude dynamics of the quadrotor are represented using modified Rodrigues parameters. Inspired by the biological trial-and-error mechanism that reinforcement learning (RL) emulates, the proposed method is developed by integrating fuzzy logic systems (FLSs) with RL. To enhance the autonomous learning capability and tracking performance of the UAV system, actor–critic (AC) learning is introduced as an effective RL method. A cost function defined in terms of tracking errors is introduced, and an FLS is incorporated into the critic to approximate the cost function for performance evaluation. The actor is responsible for generating the control input based on the critic signals. Concurrently, another FLS is employed to approximate system uncertainties and actuator bias faults. Furthermore, to meet increasingly stringent control requirements, performance constraints are imposed to guarantee prescribed tracking performance. The system stability and convergence of tracking errors are analyzed using Lyapunov stability theory. Finally, simulations are conducted to verify the effectiveness of the proposed adaptive fault-tolerant attitude control scheme.