Drone Visual Active Tracking aims to autonomously follow a target object by controlling the motion system based on visual observations, providing a more practical solution for effective tracking in dynamic environments. However, accurate Drone Visual Active Tracking using reinforcement learning remains challenging due to the absence of a unified benchmark and the complexity of open-world environments with frequent interference. To address these issues, we pioneer a systematic solution. First, we propose DAT, the first open-world drone active air-to-ground tracking benchmark. It encompasses 24 city-scale scenes, featuring targets with human-like behaviors and high-fidelity dynamics simulation. DAT also provides a digital twin tool for unlimited scene generation. Additionally, we propose a novel reinforcement learning method called GC-VAT, which aims to improve the performance of drone tracking targets in complex scenarios. Specifically, we design a Goal-Centered Reward to provide precise feedback across viewpoints to the agent, enabling it to expand perception and movement range through unrestricted perspectives. Inspired by curriculum learning, we introduce a Curriculum-Based Training strategy that progressively enhances the tracking performance in complex environments. Besides, experiments on simulator and real-world images demonstrate the superior performance of GC-VAT, achieving a Tracking Success Rate of approximately 72% on the simulator. The benchmark and code are available at https://github.com/SHWplus/DAT_Benchmark.