The optical rotation property of a polarized alkali vapor cell is demonstrated. The polarized atomic gas chamber can be macroscopically equivalent to a Faraday polarized crystal, whose optical rotation coefficient is related to the spin precession of atoms. A novel atomic spin precession detection scheme is proposed by means of the detection of the phase difference between the left and the right circularly polarized probe lights when a circularly polarized probe light is propagating through the vapor cell. Based on the modified all-fiber reflective Sagnac interferometer, the fiber atomic spin precession detection system is built and the detection of spin precession signals in the spin exchanged relaxation free states is realized by a circularly polarized light. The detection scheme is verified and the gyroscopic effect is realized on the experimental platform of an atomic spin gyroscope. The experimental results confirm that the proposed theory is correct. The performance of this gyroscope is preliminarily tested and its zero-bias instability is 0.29 (°)/h.