Spiking Neural Networks (SNNs), characterized by their event-driven computation and low power consumption, have shown great potential for energy-efficient visual tracking on unmanned aerial vehicles (UAVs). However, existing SNN-based trackers often rely on costly event cameras, which limits their deployment on standard RGB-camera UAV platforms. To address this limitation, we propose STATrack, a fully spiking neural network framework for UAV visual tracking using only RGB inputs. To the best of our knowledge, this is the first study to explore fully spiking neural networks for RGB-based UAV visual tracking. To alleviate target semantic degradation caused by spike discretization and reduce background interference in UAV scenes, we introduce an Adaptive Mutual Information Maximization (AMIM) mechanism. AMIM maximizes the mutual information between template inputs and their deep target-aware features, encouraging the spiking backbone to preserve discriminative target semantics. In addition, a sample-difficulty-aware dynamic weighting strategy is designed to adaptively adjust the mutual information constraint during training. Extensive experiments on four widely used UAV tracking benchmarks demonstrate that STATrack achieves state-of-the-art tracking performance with low theoretical energy consumption, highlighting its potential for energy-constrained UAV applications.