We build a resonant fiber optic gyro based on Kagome hollow-core fiber. A semi-bulk cavity architecture based on an 18-m-long Kagome fiber permits achieving a cavity finesse of 23 with a resonance linewidth of 700 kHz. An optimized Pound-Drever-Hall servo-locking scheme is used to probe the cavity in reflection. Closed-loop operation of the gyroscope permits reaching an angular random walk as small as 0.004°/h and a bias stability of 0.45°/h over 0.5 s of integration time.