Rotate vector (RV) reducers are widely used as the joints of industrial robots. Due to RV reducers often work in a reciprocating condition, it makes the corresponding vibration for fault detection is incomplete since the incompletely rotation of the output shaft. Thus, traditional methods such as the vibration separation (VS) cannot be used to detect the tooth fault of planet gear in RV reducer. Moreover, few literatures reported the tooth fault detection of RV reducer without disassembly. To address this issue, a method for detecting the planet gear tooth root crack fault of RV reducers is proposed in this paper. It combines the improved compute order tracking (ICOT), the signal extraction and reconstruction of planet gear, and the synchronous averaging (SA). The ICOT is utilized to obtain data blocks of each tooth of the gear on the reference shaft while eliminating the inevitable speed fluctuations. Subsequently, the tooth mapping relationship between the planet gear and sun gear can be calculated by the planetary meshing structure. Then, the data block of each tooth of the planet gear can be extracted from the resampled vibration. Next, data blocks of the planet gear can be constructed into a synthetic signal according to the tooth mapping relationship. Furthermore, the SA is applied to enhance the signal-noise ratio (SNR) of the synthetic signal. Finally, spectral analysis is utilized to expose the fault characteristics. The comparative experiment with the normal and faulty planet gear in an RV reducer test rig validated the effectiveness of the proposed method.