Faraday magneto-optic effect of fiber optic gyroscope(FOG) is nonreciprocal error source that affects the performance of FOG, especially the precision of FOG. The magnetic sensitivity mechanism of FOG is introduced in this paper and the main source of radial and axial magnetic sensitivity error is analyzed. The circular birefringence of the fiber is improved by twisting. With coupled wave equations of twist fiber, an expression that can evaluate circular birefringence degree of fiber is obtained. Based on the above analysis, this paper puts forward an approach that a length of reverse twist fiber is spliced onto the original fiber coil of FOG. This approach can produce high circular birefringence. The reciprocity phase of original fiber coil is compensated so that the purpose that restrains magnetic sensitivity error of FOG is achieved. The feasibility of this method is discussed.