A new approach to generate beam steering for the circularly polarized (CP) antenna array without phase shift circuits is proposed. The proposed approach is a low cost one compared with those with phase shifters. It is found that in spherical coordinate system ( $r$ , $\theta $ , and $\varphi $ ), for any constant $r$ and $\theta $ , as $\varphi $ varies from 0 to $2\pi $ , the phase of the CP antenna’s copolarized far field will progress linearly by $2\pi $ , and the magnitude is constant. If a CP antenna is rotated around its own phase center by certain degrees, there is a phase difference between the copolarized electric far fields generated by the antenna before and after rotation. An $N \times N$ array with such CP antennas elements is analyzed. The array can generate beam steering with different rotation angles of adjacent elements. The beam-steering mechanism is discussed from the orthogonal electric current elements and array perspective. Then, a $4 \times 4$ planar spiral array is designed to verify the mechanism. The array has a good beam-steering characteristic within $X$ -band. At the planes of $\varphi = 0^{\circ }$ , 45°, and 90°, the mainlobe can be scanned from −25° to +24°, −36° to +35°, and −24° to +25°, respectively.