Most existing RGB-T tracking networks extract modality features in a separate manner, which lacks interaction and mutual guidance between modalities. This limits the network's ability to adapt to the diverse dual-modality appearances of targets and the dynamic relationships between the modalities. Additionally, the three-stage fusion tracking paradigm followed by these networks significantly restricts the tracking speed. To overcome these problems, we propose a unified single-stage Transformer RGB-T tracking network, namely USTrack, which unifies the above three stages into a single ViT (Vision Transformer) backbone with a dual embedding layer through self-attention mechanism. With this structure, the network can extract fusion features of the template and search region under the mutual interaction of modalities. Simultaneously, relation modeling is performed between these features, efficiently obtaining the search region fusion features with better target-background discriminability for prediction. Furthermore, we introduce a novel feature selection mechanism based on modality reliability to mitigate the influence of invalid modalities for prediction, further improving the tracking performance. Extensive experiments on three popular RGB-T tracking benchmarks demonstrate that our method achieves new state-of-the-art performance while maintaining the fastest inference speed 84.2FPS. In particular, MPR/MSR on the short-term and long-term subsets of VTUAV dataset increased by 11.1$\%$/11.7$\%$ and 11.3$\%$/9.7$\%$.