Neurophysiological research has shown that auditory and motor systems interact during movement to rhythmic auditory stimuli through a process called entrainment. This study explores the neural oscillations underlying auditory-motor entrainment using electroencephalography. Forty young adults were randomly assigned to one of two control conditions, an auditory-only condition or a motor-only condition, prior to a rhythmic auditory-motor synchronization condition (referred to as combined condition). Participants assigned to the auditory-only condition auditory-first group) listened to 400 trials of auditory stimuli presented every 800 ms, while those in the motor-only condition (motor-first group) were asked to tap rhythmically every 800 ms without any external stimuli. Following their control condition, all participants completed an auditory-motor combined condition that required tapping along with auditory stimuli every 800 ms. As expected, the neural processes for the combined condition for each group were different compared to their respective control condition. Time-frequency analysis of total power at an electrode site on the left central scalp (C3) indicated that the neural oscillations elicited by auditory stimuli, especially in the beta and gamma range, drove the auditory-motor entrainment. For the combined condition, the auditory-first group had significantly lower evoked power for a region of interest representing sensorimotor processing (4–20 Hz) and less total power in a region associated with anticipation and predictive timing (13–16 Hz) than the motor-first group. Thus, the auditory-only condition served as a priming facilitator of the neural processes in the combined condition, more so than the motor-only condition. Results suggest that even brief periods of rhythmic training of the auditory system leads to neural efficiency facilitating the motor system during the process of entrainment. These findings have implications for interventions using rhythmic auditory stimulation.