Graph Neural Networks (GNNs) have recently achieved good performance in many predictive tasks involving graph-structured data. However, the majority of existing models consider static graphs only and do not support training on graph streams. While inductive representation learning can generate predictions for unseen vertices, these are only accurate if the learned graph structure and properties remain stable over time. In this paper, we study the problem of employing experience replay to enable continuous graph representation learning in the streaming setting. We propose two online training methods, Random-Based Rehearsal-RBR, and Priority-Based Rehearsal-PBR, which avoid retraining from scratch when changes occur. Our algorithms are the first streaming GNN models capable of scaling to million-edge graphs with low training latency and without compromising accuracy. We evaluate the accuracy and training performance of these experience replay methods on the node classification problem using real-world streaming graphs of various sizes and domains. Our results demonstrate that PBR and RBR achieve orders of magnitude faster training as compared to offline methods while providing high accuracy and resiliency to concept drift.