Quantum networks are becoming increasingly important because of advancements in quantum computing and quantum sensing, such as recent developments in distributed quantum computing and federated quantum machine learning. Routing entanglement in quantum networks poses several fundamental as well as technical challenges, including the high dynamicity of quantum network links and the probabilistic nature of quantum operations. Consequently, designing hand-crafted heuristics is difficult and often leads to suboptimal performance, especially if global network topology information is unavailable. In this paper, we propose RELiQ, a reinforcement learningbased approach to entanglement routing that only relies on local information and iterative message exchange. Utilizing a graph neural network, RELiQ learns graph representations and avoids overfitting to specific network topologies – a prevalent issue for learning-based approaches. Our approach, trained on random graphs, consistently outperforms existing local information heuristics and learning-based approaches when applied to random and real-world topologies. When compared to global information heuristics, our method achieves similar or superior performance because of its rapid response to topology changes.