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Users are daily exposed to a large volume of harmful content on various social network platforms. One solution is developing online moderation tools using Machine Learning techniques. However, the processing of user data by online platforms requires compliance with privacy policies. Federated Learning (FL) is an ML paradigm where the training is performed locally on the users' devices. Although the FL framework complies, in theory, with the GDPR policies, privacy leaks can still occur. For instance, an attacker accessing the final trained model can successfully perform unwanted inference of the data belonging to the users who participated in the training process. In this paper, we propose a privacy-preserving FL framework for online content moderation that incorporates Differential Privacy (DP). To demonstrate the feasibility of our approach, we focus on detecting harmful content on Twitter - but the overall concept can be generalized to other types of misbehavior. We simulate a text classifier - in FL fashion - which can detect tweets with harmful content. We show that the performance of the proposed FL framework can be close to the centralized approach - for both the DP and non-DP FL versions. Moreover, it has a high performance even if a small number of clients (each with a small number of data points) are available for the FL training. When reducing the number of clients (from 50 to 10) or the data points per client (from 1K to 0.1K), the classifier can still achieve ~81% AUC. Furthermore, we extend the evaluation to four other Twitter datasets that capture different types of user misbehavior and still obtain a promising performance (61% - 80% AUC). Finally, we explore the overhead on the users' devices during the FL training phase and show that the local training does not introduce excessive CPU utilization and memory consumption overhead.