Hollow core photonic crystal fiber, as a new type of special fiber, can be used in resonant fiber gyroscopes to prepare high-performance miniaturized resonant cavities, with strong environmental anti-interference ability and the advantage of reducing nonlinear optical noise. This paper proposes a single beam splitter reflective spatial micro mirror coupling scheme on a silicon-based optical platform to address the issue of excessive fusion losses in hollow core optical fibers. The scheme achieves a small-sized and low coupling loss hollow core photonic crystal fiber resonant cavity, while providing a compensation interface for the stability of the incoming optical power. Combined with an optical power feedback module, it can effectively suppress optical Kerr noise in the system. The characteristics of miniaturization and temperature insensitivity of hollow core photonic crystal fiber resonant cavity are studied. Finally, the resonant cavity is tested, and the results show that the coupling loss of the resonant cavity is 0.28 dB, and the output precision is 19.4, which is currently the best level among similar schemes. After feedback compensation, the forward and backward light power difference is 17.5 nW, and the system detection accuracy determined by optical Kerr noise reaches 0.07 °/h, meeting the high-precision gyroscope accuracy requirements.