A closed-loop resonator fiber optic gyro (R-FOG) with a precisely controlled bipolar digital serrodyne phase modulation scheme is experimentally demonstrated. The serrodyne modulation scheme serves multiple functions in the R-FOG, from reducing the backscattering induced performance degradation to achieving the closed-loop operation. To improve the backscattering suppression efficiency, a precise amplitude adjustment method using a gain variable amplifier and the oversampling technique is utilized to control the waveform of the bipolar digital serrodyne phase modulation. Compared with the amplitude control via adjusting the digital gain of the function generator, improved bias stability is realized. Moreover, the closed-loop operation is needed for the R-FOG to achieve high linearity in a wide dynamic range as the frequencies of both the clockwise (CW) and the counter clockwise (CCW) lightwaves are maintained at the resonator's resonant frequency. To balance the resonant frequency difference, an additional bipolar digital serrodyne waveform, with the slope proportional to the rotation speed to compensate for the resonant frequency difference, is superimposed on the original bipolar digital serrodyne waveform. Measurement results of different rotation speeds show good linearity thanks to the adoption of closed-loop operation.