Resonator fiber optic gyro (R-FOG) is a novel optical rotation sensor whose resonant frequency is changed due to the Sagnac effect. In R-FOG using phase modulation (PM) spectroscope technology, a digital synchronous detection circuit based on the coordinate rotation digital computer (CORDIC) algorithm is studied. It can make the R-FOG system more stable and flexible using a single field programmable gate array (FPGA) to realize the modulation signal generation, synchronous demodulation and signal processing synchronously. The frequency synthesis technology and synchronous detection circuit based on CORDIC algorithm are analyzed and tested. Applying the digital synchronous detection circuit to the R-FOG system, the gyro rotation signal is observed successfully.