We developed a pixel-readout micro-pixel chamber (mu-PIC) as an astronomical X-ray polarimeter and demonstrated its ability to achieve a higher sensitivity than a strip-readout one by a beam test. The mu-PIC is one of the micropattern gas detectors that have been developed so far. However, its readout was of the strip type. This limits the sensitivity to polarization because it cannot determine the polarization angle uniquely without rotating the detector. Thus, we started developing the pixel-readout type of mu-PIC. A beam test at a synchrotron-radiation facility was carried out to examine the performance for polarimetry. Without rotating the detector, we successfully detected the polarization angle. The modulation factor for 8 keV X-rays in a neon-based mixture was 0.12 +/- 0.03, which is at the same level as that of the strip-type mu-PIC, and 0.07 +/- 0.01 at 15 keV in an argon-based mixture. These results indicate the ability of the new mu-PIC to achieve a higher sensitivity to X-ray polarization than that obtainable with the strip-type mu-PIC.