With the capacity to capture high-order collaborative signals, Graph Neural Networks (GNNs) have emerged as powerful methods in Recommender Systems (RS). However, their efficacy often hinges on the assumption that training and testing data share the same distribution (\aka IID assumption), and exhibits significant declines under distribution shifts. Distribution shifts commonly arises in RS, often attributed to the dynamic nature of user preferences or ubiquitous biases during data collection in RS. Despite its significance, researches on GNN-based recommendation against distribution shift are still sparse. To bridge this gap, we propose Distributionally Robust GNN (DR-GNN) that incorporates Distributional Robust Optimization (DRO) into the GNN-based recommendation. DR-GNN addresses two core challenges: 1) To enable DRO to cater to graph data intertwined with GNN, we reinterpret GNN as a graph smoothing regularizer, thereby facilitating the nuanced application of DRO; 2) Given the typically sparse nature of recommendation data, which might impede robust optimization, we introduce slight perturbations in the training distribution to expand its support. Notably, while DR-GNN involves complex optimization, it can be implemented easily and efficiently. Our extensive experiments validate the effectiveness of DR-GNN against three typical distribution shifts. The code is available at https://github.com/WANGBohaO-jpg/DR-GNN.