Microstrip square patch antennas with arc shaped grooves on the four edges are proposed and investigated. By cutting asymmetrical grooves on the square microstrip antenna, the single-feed microstrip antennas are realized for circularly polarized radiation. In this paper, several designs with different groove dimensions are listed, and all give good performance, providing a large flexibility in design and fabrication. Experimental results show that the proposed design has good circularly polarized radiation and an antenna-size reduction of about 35% compared to the conventional square patch antenna at a given operating frequency. Detailed results are presented and analyzed.