For an interferometric fiber-optic gyroscope (IFOG), the angle random walk, which represents the sensitivity of rotation detection, is mainly limited by the relative intensity noise (RIN) of a broadband source. Using a single-mode fiber ring resonator (SM-FRR) to filter the spectrum of a broadband light source is a common strategy for reducing the RIN at the proper IFOG frequency. However, this method depends on the polarization cross-coupling within the SM-FRR. We model the effect of polarization cross-coupling on the SM-FRR. Then, to further reduce the RIN, we introduce a polarization-maintaining fiber ring resonator (PM-FRR), which mitigates the effect of polarization cross-coupling on the SM-FRR. Using the PM-FRR as a spectrum filter, the RIN is reduced to -143 dB/Hz, with a reduction ratio of 25 dB, and the angle random walk in the IFOG is improved by over five times from 1.17 to 0.223 mdeg/h1/2 using a 2.1 km sensing coil.