Resonator fiber optic gyro (R-FOG) is a novel optical sensor whose resonant frequency is changed due to the Sagnac effect. The detection technique and system noises affect the detection precision greatly. In the R-FOG based on the phase modulation spectroscopy technique, not only the optical power difference between the clockwise (CW) and counterclockwise (CCW) light waves induces the bias drift, but also the two different modulation indexes do. The bias drift caused by optical Kerr effect is indistinguishable from the rotational-induced Sagnac frequency shift. Using the optical field overlapping method, the analytical expression for the rotation-rate error due to the optical Kerr effect is derived. For the bias drift caused by the optical Kerr effect does not change with the rotation-rate, using a simple open-loop operation, the drift caused by the optical Kerr effect is observed in the gyro output curve.