In resonator micro-optic gyros (RMOGs), the interference between the backreflection light beam of one pathway and the signal light beam of the other pathway deteriorates the gyro output waveforms, resulting in severe reduction in the gyro's accuracy. In this paper, an integer period sampling (IPS) method is introduced to minimize the sampling error caused by backreflection in RMOG for the first time to our knowledge. The experimental results show that both the bias repeatability and the short-term bias stability become better when the IPS condition is satisfied. A bias stability of 0.41°/s over one hour with an integration time of 10 s has been realized in a RMOG that employs a silica waveguide ring resonator.