We present a novel approach for multiview canonical correlation analysis based on a variational graph neural network model. We propose a nonlinear model which takes into account the available graph-based geometric constraints while being scalable to large-scale datasets with multiple views. This model combines the probabilistic interpretation of CCA with an autoencoder architecture based on graph convolutional neural network layers. Experiments with the proposed method are conducted on classification, clustering, and recommendation tasks on real datasets. The algorithm is competitive with state-of-the-art multiview representation learning techniques, in addition to being scalable and robust to instances with missing views.