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Optical beams carrying orbital angular momentum (OAM) have received much attention due to the prospects of their use in terahertz communications, biomedical engineering, and imaging. Here we propose an antenna design for the generation of multiple beams carrying OAM with different topological states at the same frequency. The proposed OAM generator is based on a compact set of microstrip ring-shaped resonators. An analytical solution for the radiated field of a single circular ring resonator antenna is derived involving the cavity model and the magnetic current approach. To verify our theoretical description, the numerical full-wave simulation is performed for an actual size OAM generator with the use of the ANSYS HFSS electromagnetic solver, and an antenna prototype operating in the microwave band is fabricated and tested. Conditions of the antenna operation in the combined OAM and mode-division multiplexing (OAM-MDM) regimes are discussed. Obtained results prove that the proposed antenna can be used as a compact and low-cost generator of multiple beams with different OAM states.