We propose and experimentally demonstrate a polarization-insensitive single sideband modulator based on silicon microring modulators (MRM). The proposed modulator splits and modulates the two orthogonal polarization states of an input laser in a loopback structure, with an on-chip silicon polarization splitter rotator (PSR), overcoming the polarization dependence of the silicon photonic modulator. The IQ configuration of the modulator enables single sideband modulation, thus improving the resistance of the modulated signal to chromatic dispersion and extending the transmission reach. The adoption of an MRM relieves the bandwidth limitation in polarizationdiverse versions of SiP Mach-Zehnder modulators (MZM). Our experiments validate the proposed modulator polarization insensitivity and transmission performance.