The design of Graph Transformers (GTs) generally neglects considerations for fairness, resulting in biased outcomes against certain sensitive subgroups. Since GTs encode graph information without relying on message-passing mechanisms, conventional fairness-aware graph learning methods cannot be directly applicable to address these issues. To tackle this challenge, we propose FairGT, a Fairness-aware Graph Transformer explicitly crafted to mitigate fairness concerns inherent in GTs. FairGT incorporates a meticulous structural feature selection strategy and a multi-hop node feature integration method, ensuring independence of sensitive features and bolstering fairness considerations. These fairness-aware graph information encodings seamlessly integrate into the Transformer framework for downstream tasks. We also prove that the proposed fair structural topology encoding with adjacency matrix eigenvector selection and multi-hop integration are theoretically effective. Empirical evaluations conducted across five real-world datasets demonstrate FairGT's superiority in fairness metrics over existing graph transformers, graph neural networks, and state-of-the-art fairness-aware graph learning approaches.