External control arms (ECA) can inform the early clinical development of experimental drugs and provide efficacy evidence for regulatory approval in non-randomized settings. However, the main challenge of implementing ECA lies in accessing real-world data or historical clinical trials. Indeed, data sharing is often not feasible due to privacy considerations related to data leaving the original collection centers, along with pharmaceutical companies' competitive motives. In this paper, we leverage a privacy-enhancing technology called federated learning (FL) to remove some of the barriers to data sharing. We introduce a federated learning inverse probability of treatment weighted (IPTW) method for time-to-event outcomes called FedECA which eases the implementation of ECA by limiting patients' data exposure. We show with extensive experiments that FedECA outperforms its closest competitor, matching-adjusted indirect comparison (MAIC), in terms of statistical power and ability to balance the treatment and control groups. To encourage the use of such methods, we publicly release our code which relies on Substra, an open-source FL software with proven experience in privacy-sensitive contexts.