Autonomous underwater vehicles (AUVs) are instrumental for data offloading in underwater sensor networks (USNs). With high data rate capacity at transmission ranges in the order of several tens of meters, visible light communication (VLC) is well-positioned to serve as a wireless link between the AUV and sensor nodes. In this paper, we consider a USN network where an AUV is used for data retrieval from the sensors through VLC link. We formulate the design of optimal AUV trajectory as an optimization problem to minimize the AUV energy consumption under data rate constraints imposed by the VLC link and in the presence of ocean currents. Our numerical results demonstrate that our proposed trajectory is reactive to ocean currents and brings significant reductions in energy consumption and mission time of the AUVs, in particular for USN scenarios with a large number of sensor nodes.