Existing methods for tracking mobile sinks in Wireless Sensor Networks (WSNs) often incur considerable energy consumption and overhead. To address this issue, we propose a Detour-Aware Mobile Sink Tracking (DAMST) method via analysis of movement angle changes of mobile sinks, for collecting data in a low-overhead and energy efficient way. In the proposed method, while a mobile sink passes through a region, it appoints a specific node as a region agent to collect information of the whole region, and records nodes near or on its trajectory as footprints. If it needs information from the region agent in a future time it will construct an energy efficient path from the region agent to itself by calculating its own movement angles according to the footprints, as well as getting rid of detours by analyzing these movement angles. Finally, the performance of the tracking method is evaluated systematically under different trajectory patterns and footprint appointment intervals. The simulation results consolidate that DAMST has advantages in reducing energy consumption and data overhead.