Learning to predict missing links is important for many graph-based applications. Existing methods were designed to learn the association between observed graph structure and existence of link between a pair of nodes. However, the causal relationship between the two variables was largely ignored for learning to predict links on a graph. In this work, we visit this factor by asking a counterfactual question: "would the link still exist if the graph structure became different from observation?" Its answer, counterfactual links, will be able to augment the graph data for representation learning. To create these links, we employ causal models that consider the information (i.e., learned representations) of node pairs as context, global graph structural properties as treatment, and link existence as outcome. We propose a novel data augmentation-based link prediction method that creates counterfactual links and learns representations from both the observed and counterfactual links. Experiments on benchmark data show that our graph learning method achieves state-of-the-art performance on the task of link prediction.