Radio waves carrying orbital angular momentum (OAM) have been intensively studied in recent years with respect to generation, propagation, and communication. In this article, the effect of an infinite ground on OAM wave propagation and communication is investigated numerically using the method of moments (MoM). A circular array of half-wavelength dipoles is taken as a uniform circular array, for the generation and reception of OAM waves. First, electromagnetic image theory is adopted for analysis and numerical investigation of image OAM arrays and their influence of reflections from the ground plane. Employing MoM and mixed-mode scattering parameters, the impact of the ground plane on wireless communication is further explored by varying the communication distances between the transmitting and receiving arrays, heights of OAM arrays above the ground, and array orientations. Compared to OAM-based communication in free space, the effect of the ground plane turns out to be considerable. Specifically, it was found that OAM-based communication not only suffers from destructive influence due to reflections from the ground but also from reduced mode isolation. The results obtained in this article will be fundamental for optimizing OAM-based communication in a realistic environment.