We report a novel approach for characterization of terahertz (THz) antennas using the photoinduced coded-aperture imaging (PI-CAI) technique. For a prototype demonstration, a WR-1.5 (500-750 GHz) diagonal horn antenna has been fully characterized. The THz beam radiated from the antenna was imaged using the PI-CAI technique at different distances from the antenna aperture. The measured beam profiles show near-Gaussian shapes, with the expected propagation properties. The far-field antenna radiation patterns were then extracted from the far-field beam image and compared with conventional measurement results, theoretical calculation and full-wave simulation. Finally, the antenna Gaussian coupling efficiency was calculated to be $83% based on the two-dimensional (2-D) beam mapping technique. Antenna radiation parameters obtained using the above approach show good agreement with published literature and manufacturer datasheets, demonstrating the potential of the PI-CAI approach for fast and accurate characterization of THz antennas.