In this paper, a novel scheme to implement an optical single sideband (OSSB) polarization modulator (PolM) is proposed and theoretically investigated. The proposed structure contains two dual-drive Mach-Zehnder modulators inside a Mach-Zehnder interferometer whose input/output optical Y-couplers are replaced by two optical polarization beam splitters/polarization beam combiners. It is shown that by applying four equal power radio-frequency signals with appropriate phases, an OSSB polarization-modulated signal is generated. In addition, $(4n+3)$(4n+3)th-order sidebands, where ${n}$n is an integer, are suppressed without the need for an optical filter. The proposed OSSB PolM can find many applications in microwave photonic (MWP) systems. For instance, by using the proposed OSSB PolM, an OSSB modulator with tunable optical carrier-to-sideband ratio (OCSR), an OSSB-suppressed carrier modulator/optical frequency shifter with ultralow spurious sidebands, and an MWP phase shifter with 360° tunable phase shifts, are proposed and theoretically investigated. Simulation results using commercial software are also presented, which are in good agreement with analytical results.