This article investigates the fixed-time attitude control problem of quadrotor unmanned aerial vehicles (QUAVs) subject to stochastic disturbances. A fixed-time stability criterion for stochastic systems, which can compress the upper bound of the convergence time compared with the fixed-time stable Lyapunov theorem commonly used in the existing works, is proposed and theoretically proofed. The impact of stochastic disturbances on a QUAV is considered and a stochastic model of the attitude system of a QUAV is established. Based on the proposed criterion, a novel fixed-time attitude tracking controller for QUAV is designed, which can theoretically ensure the stability of attitude tracking within a fixed-time frame. To demonstrate the effectiveness of the controller, a simulation example is presented. A simulation comparison of different methods is also conducted. By artificially adding stochastic disturbances to the attitude angular velocity signals from sensors, an experiment is carried out on the three-DoF QUAV experimental platform. The experimental results show the feasibility of the designed control method in practical application.