Resonator fiber optic gyro (R-FOG) is an inertial rotation sensor with high accuracy which is based on the Sagnac effect. The signal detection system has important role in the R-FOG. The detecting precision influences the maximum resolution of the gyro directly. The fiber ring resonator is the core-sensing element in the R-FOG. This paper presents the scheme to detect the resonance point using two-frequency serrodyne modulation, and uses the Lorentzian function to describe the expression of the output power at the exit port of the fiber ring resonator taking the temporal coherence of the laser into account. According to near linear relationship between amplitude of the square waveform and the resonant frequency deviation near the resonant point, frequency feedback time after time is used for frequency tracking for both clockwise (CW) and counterclockwise (CCW) waves. Therefore, complex root finding process can be avoided. Simulation shows that both CW and CCW waves can be locked at the resonance frequency of the resonator quickly by frequency feedback operation.