Fair spectral clustering ensures a balanced representation of sensitive groups across clusters and has recently attracted significant attention. Most existing fair spectral clustering methods follow a three-step approach, i.e., graph construction, fair spectral embedding, and k-means clustering. This often leads to sub-optimal results due to the noisy information and high dimensional representation during graph construction. Additionally, existing fair spectral clustering methods fail to jointly utilize the graph information and embedding matrices, which results in further degradation of clustering performance. This paper addresses these limitations by introducing a fair one-step spectral rotation clustering method, which utilizes a novel Group Fairness Term (GFT) and integrates all independent stages of spectral clustering into a unified framework via adaptive graph learning. This GFT is capable of producing clusters with a balanced representation of sensitive groups. Furthermore, this paper also introduces an algorithm using the alternating direction method of the multiplier framework to update the variables. Extensive experiments have been performed on various datasets and compared with bench-marked methods to validate the efficacy of the proposed method.