With advances in nanotechnology, emerging plasmonic nano-optical applications, such as all-optical magnetic recording, require circularly-polarized electromagnetic radiation beyond the diffraction limit. In this study, a plasmonic cross-dipole nano-antenna is investigated to obtain a circularly polarized near-field optical spot with a size smaller than the diffraction limit of light. The performance of the nano-antenna is investigated through numerical simulations. In the first part of this study, the nano-antenna is illuminated with a diffraction-limited circularly-polarized radiation to obtain circularly polarized optical spots at nanoscale. In the second part, diffraction limited linearly polarized radiation is used. An optimal configuration for the nano-antenna and the polarization angle of the incident light is identified to obtain a circularly polarized optical spot beyond the diffraction limit from a linearly polarized diffraction limited radiation.