Link prediction aims to reveal missing edges in a graph. We address this task with a Gaussian process that is transformed using simplified graph convolutions to better leverage the inductive bias of the domain. To scale the Gaussian process model to large graphs, we introduce a variational inducing point method that places pseudo inputs on a graph-structured domain. We evaluate our model on eight large graphs with up to thousands of nodes and report consistent improvements over existing Gaussian process models as well as competitive performance when compared to state-of-the-art graph neural network approaches.