Wireless transmission based on orbital angular momentum (OAM) can improve spectrum utilization, but it requires effective OAM mode generation. Using the characteristic mode analysis, it is easy to obtain degenerate mode distributions of the symmetric rectangular patch. The coupling phase difference of 90° between two degenerate modes can be implemented by disrupting the symmetry. In that case, a single feed structure located at the common position of equal mode current amplitudes can excite two degenerate modes to synthesize OAM modes. When the fundamental degenerate modes of the rectangular patch antenna are used, only the field component along the beam direction has the characteristics of the first order OAM. To achieve higher order OAM modes, the patch structure should be further adjusted. By introducing slots in the patch edges and grounding the patch at its center, the single‐fed rectangular patch antenna can radiate the vortex wave carrying the second order OAM. Furthermore, the OAM mode performance such as mode purity can be analyzed by the modal excitation coefficients.