The Fair Graph Anomaly Detection (FairGAD) problem aims to accurately detect anomalous nodes in an input graph while ensuring fairness and avoiding biased predictions against individuals from sensitive subgroups such as gender or political leanings. Fairness in graphs is particularly crucial in anomaly detection areas such as misinformation detection in search/ranking systems, where decision outcomes can significantly affect individuals. However, the current literature does not comprehensively discuss this problem, nor does it provide realistic datasets that encompass actual graph structures, anomaly labels, and sensitive attributes for research in FairGAD. To bridge this gap, we introduce a formal definition of the FairGAD problem and present two novel graph datasets constructed from the globally prominent social media platforms Reddit and Twitter. These datasets comprise 1.2 million and 400,000 edges associated with 9,000 and 47,000 nodes, respectively, and leverage political leanings as sensitive attributes and misinformation spreaders as anomaly labels. We demonstrate that our FairGAD datasets significantly differ from the synthetic datasets used currently by the research community. These new datasets offer significant values for FairGAD by providing realistic data that captures the intricacies of social networks. Using our datasets, we investigate the performance-fairness trade-off in eleven existing GAD and non-graph AD methods on five state-of-the-art fairness methods, which sheds light on their effectiveness and limitations in addressing the FairGAD problem.