To address the limitations of single-element in independently estimating the direction of arrival (DOA) of underwater targets, as well as the positional deviations caused by ocean current disturbances during underwater unmanned vehicle (UUV) operations, this paper proposes a passive synthetic aperture DOA estimation method. The method incorporates motion offset compensation and leverages deep learning to enhance estimation accuracy under non-ideal motion conditions. The proposed method first employs synthetic aperture techniques to expand the array aperture, enabling a single-element to achieve DOA estimation. By constructing virtual elements and integrating temporal and spatial information, the motion offset angles between adjacent synthesized elements are estimated. These estimated angles are used to compensate for phase errors caused by element displacement, resulting in effective aperture synthesis. Finally, a deep learning model is introduced to perform DOA estimation. Simulation results demonstrate that the proposed approach achieves a 97.6% improvement in DOA estimation accuracy compared to the traditional MUSIC algorithm without motion offset compensation.