We analytically and numerically study the emission properties of an electric dipole coupled to a plasmonic spiral structure with different pitch. As a transmitting antenna, the spiral structure couples the radiation from the electric dipole into circularly polarized emitted photons in the far field. The spin carried by the emitted photons is determined by the handedness of the spiral antenna. By increasing the spiral pitch in the unit of surface plasmon wavelength, these circularly polarized photons also gain orbital angular momentum with different topological charges. This phenomenon is attributed to the presence of a geometric phase arising from the interaction of light from point source with the anisotropic spiral structure. The circularly polarized vortex emission from such optically coupled spiral antenna also has high directivity, which may find important applications in quantum optical information, single molecule sensing, and integrated photonic circuits.