Calibrating the phase in integrated optical phased arrays (OPAs) is a crucial procedure for addressing phase errors and achieving the desired beamforming results. In this paper, we introduce a novel phase calibration methodology based on a deep neural network (DNN) architecture to enhance beamforming in integrated OPAs. Our methodology focuses on precise phase control, individually tailored to each of the 64 OPA channels, incorporating electro-optic phase shifters. To effectively handle the inherent complexity arising from the numerous voltage set combinations required for phase control across the 64 channels, we employ a tandem network architecture, further optimizing it through selective data sorting and hyperparameter tuning. To validate the effectiveness of the trained DNN model, we compared its performance with 20 reference beams obtained through the hill climbing algorithm. Despite an average intensity reduction of 0.84 dB in the peak values of the beams compared to the reference beams, our experimental results demonstrate substantial agreements between the DNN-predicted beams and the reference beams, accompanied by a slight decrease of 0.06 dB in the side-mode-suppression-ratio. These results underscore the practical effectiveness of the DNN model in OPA beamforming, highlighting its potential in scenarios that necessitate the intelligent and time-efficient calibration of multiple beams.