The problem of attitude tracking control for spacecraft with limited communication rate is addressed in this article. To reduce the communication burden, an adaptive event-triggered control scheme is proposed. In the control scheme, only the sampling states at the event-triggering instants are sent to the control module, which can considerably decrease the data transmission rate. To address the inertia uncertainties and external disturbances, a radial basis function neural network (NN) is introduced. The bound of the uncertainties and disturbances is estimated for the proposed control scheme, which can simplify the NN and reduce the computation. Since the event-triggered error signal is discontinuous due to the event-triggered mechanism, the closed-loop system is formulated as an impulsive dynamical system to obtain the stability properties of the system. Finally, simulation results are given to demonstrate the effectiveness of the proposed control scheme.