Molecular docking is a key method in computer-aided drug design, where the rapid identification of drug candidates is crucial for combating diseases. AutoDock is a widely-used molecular docking program, having an irregular structure characterized by a divergent control flow and compute-intensive calculations. This work investigates porting AutoDock to the SX-Aurora TSUBASA vector engine and evaluates the achievable performance on a number of real-world input compounds. In particular, we discuss the platform-specific coding styles required to handle the high degree of irregularity in both local-search methods employed by AutoDock. These Solis-Wets and ADADELTA methods take up a large part of the total computation time. Based on our experiments, we achieved runtimes on the SX-Aurora TSUBASA VE 20B that are on average 3 x faster than on modern dual-socket 64-core CPU nodes. Our solution is competitive with V100 GPUs, even though these already use newer chip fabrication technology (12 nm vs. 16 nm on the VE 20B).