X-ray polarimetry in astronomy has not been exploited well, despite its importance. The recent innovation of instruments is changing this situation. We focus on a complementary MOS (CMOS) pixel detector with small pixel size and employ it as an x-ray photoelectron tracking polarimeter. The CMOS detector we employ is developed by GPixel Inc., and has a pixel size of 2.5 $mathrm{mu}$m $times$ 2.5 $mathrm{mu}$m. Although it is designed for visible light, we succeed in detecting x-ray photons with an energy resolution of 176 eV (FWHM) at 5.9 keV at room temperature and the atmospheric condition. We measure the x-ray detection efficiency and polarimetry sensitivity by irradiating polarized monochromatic x-rays at BL20B2 in SPring-8, the synchrotron radiation facility in Japan. We obtain modulation factors of 7.63% $pm$ 0.07% and 15.5% $pm$ 0.4% at 12.4 keV and 24.8 keV, respectively. It demonstrates that this sensor can be used as an x-ray imaging spectrometer and polarimeter with the highest spatial resolution ever tested.
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