In this paper, we investigate the problem of tracking the angle of arrivals (AoAs) of multi-source in millimeter wave (mmWave)-based integrated sensing and communication (ISAC) systems with multiple radio frequency (RF) chains. Considering the time-varying nature of the channel, we propose a deep neural network (DNN)-based active learning scheme for adaptive analog beamforming and multi-source AoA estimation through the probability distribution of AoA. The proposed scheme consists of a DNN-based beamformer and a beam-space multiple signal classification (MUSIC) estimator. Specifically, the DNN generates the beamformer based on the estimated AoA distributions from the previous time block, and the MUSIC estimator exploits the measured signal by the beamformer to estimate the AoAs and the AoA distributions in the current time block. We conduct simulations to evaluate the tracking performance of the proposed scheme, and we show that the proposed scheme significantly outperforms the existing codebook-based beamformer methods.