With the development of network technology, many social media are flourishing. Due to imperfect Internet regulation, the spread of false rumors has become a common problem on those social platforms. Social platforms can generate rumor data in their operation process, but existing rumor detection models are all constructed for a single social platform, which ignores the value of cross-platform rumor. This paper combines the federated learning paradigm with the bidirectional graph attention network rumor detection model and proposes the federated graph attention network(FedGAT) model for rumor detection. Taking the advantages of horizontal federated learning for cross-platform rumor detection, the security of each social platform's data information can be ensured. We construct both the server-side and client-side models as a bidirectional graph attention network rumor detection model in the federated learning paradigm framework. The local model on the client-side can train and verify the rumor data of the social platform in the iterative process, while the model on the server-side only plays the role of aggregating the characteristics of different social platform models and does not participate in the training of the model. Finally, we conduct simulation experiments on the rumor datasets and the experimental results show that the federated graph attention network model proposed in this paper is effective for cross-platform rumor detection.