The phase error imposed in optical phased arrays (OPAs) for beam scanning LiDAR is unavoidable due to minute dimensional fluctuations that occur during the waveguide manufacturing process. To compensate for the phase error, in this study, a fast-running beamforming algorithm is developed based on the rotating element vector method. The proposed algorithm is highly suitable for OPA devices comprised of polymer waveguides, where thermal crosstalk between phase modulators is suppressed effectively, allowing for each phase modulator to be controlled independently. The beamforming speed is determined by the number of phase adjustments. Hence, by using the least square approximation for a 32-channel polymer waveguide OPA device the number of phase adjustments needed to complete beamforming was reduced and the beamforming time was shortened to 16 seconds.