To improve the scale factor stability of fiber optic current sensors, effects of azimuth which is the fiber welding azimuth between a sensing fiber and a fiber quarter-wave plate are studied, so as to restrain the linear birefringence by optimizing the azimuth. Effects of optical rotatory angle which are ignored by existing azimuth optimization theory are considered and a more accurate Jones matrix model is proposed with this new variable. It is theoretically shown that the present optimization theory has some errors with the consideration of optical rotatory angle when analyzing the simulation results. The scale factor is immune to the variable linear birefringence with some optical rotatory angles. The combined optimization of the azimuth and optical rotatory angles is proposed. It can reduce the technical requirements of fibers and effectively enhance the stability of scale factors.