The rotary vector (RV) reducer, as a highly precise transmission mechanism, can lead to a series of consequential hazards when experiencing local faults. Conducting corresponding research on performance monitoring and fault diagnosis holds significant importance. In order to achieve higher diagnostic accuracy, better classification, prediction effect, and less use of sensors, this paper proposes a local fault diagnosis method of RV reducer based on Motor current signature analysis (MCSA). Firstly, the centre gear local fault electromechanical coupling model is created by combining the working principle of the servo motor, the working characteristics of the RV reducer, and the influencing factors of motor current. Then, according to the actual operating conditions of industrial robots (IRs), the corresponding experimental platform is designed and constructed, and current signals in four different modes are collected. Fast Fourier transform (FFT) is performed on the current signals to obtain frequency domain features, and the correctness of the local fault coupling model of the centre gear is experimentally verified. Finally, the time‐domain statistical features, time–frequency domain features, and CNN features of servo‐feedback current signals under different rotational speeds are extracted and used in the implementation of local fault diagnosis for the RV reducer, respectively. In this paper, it is confirmed that MCSA can be used for localized fault diagnosis of the RV reducer, and combined with a deep learning network, it can effectively predict the fault modes with an average accuracy of more than 96%.