Brillouin fiber-optic gyroscope (BFOG) is a fiber ring resonator (FRR)-based ring laser gyroscope with a large dynamic range and high sensitivity. Previous BFOGs operated under simultaneous resonance of the pump and Brillouin laser light in the FRR, resulting in complex control systems. This article introduces an asymmetric prism Mach-Zehnder interferometer coupler (APMZIC)-based FRR system, in which the coupling ratio of pump light is large, while the Brillouin laser resonates in the cavity with a negligible coupling loss, resulting in a simple control system. We analyzed the characteristics of the APMZIC and its combined resonator system both theoretically and experimentally and verified the feasibility of connecting the APMZIC with the resonant cavity of a Brillouin laser. This coupler system is compact, easy to fabricate, highly stable, and exhibits good repeatability, which are necessary for miniaturizing lasers and gyroscopes.