Fiber optic ring resonator (FRR) is the core unit of resonator fiber optic gyro (RFOG). A novel type of ring resonator of hollow core photonic bandgap fiber (HC-PBF) based on micro-optics structure is demonstrated. The normalized transfer function of such kind of FRR is built. Then simulations are done to formulate the relations of the resonator performance and the shot-noise-limited sensitivity of RFOG caused by optical parameters of FRR. The laboratory sample of HC-PBF ring resonator based on micro-optics structure is made and its performance is tested. An optimum design is put forward based on the test data. The research results provide the basis for further research of HC-PBF RFOG based on micro-optics structure.