This paper proposes DR-GNN, a distributionally robust graph-based recommendation system that integrates Distributionally Robust Optimization (DRO) into graph neural networks (GNNs) to address distribution shifts in recommendation systems. GNNs have shown strong performance in collaborative filtering but are sensitive to distribution shifts, which are common in real-world scenarios due to dynamic user preferences and data biases. DR-GNN tackles two key challenges: (1) adapting DRO to graph-structured data by reinterpreting GNNs as graph smoothing regularizers, and (2) addressing the sparsity of recommendation data by introducing perturbations to expand the training distribution's support. DR-GNN is implemented efficiently and effectively, with extensive experiments showing its superiority over existing methods under three types of distribution shifts: popularity shift, temporal shift, and exposure shift. Theoretical analysis confirms that DR-GNN's robustness is guaranteed when the divergence between training and testing distributions is bounded. DR-GNN outperforms other methods in performance and stability, demonstrating its effectiveness in handling distribution shifts in recommendation systems. The method is theoretically grounded and provides a new perspective for enhancing the robustness of graph-based recommendation systems.This paper proposes DR-GNN, a distributionally robust graph-based recommendation system that integrates Distributionally Robust Optimization (DRO) into graph neural networks (GNNs) to address distribution shifts in recommendation systems. GNNs have shown strong performance in collaborative filtering but are sensitive to distribution shifts, which are common in real-world scenarios due to dynamic user preferences and data biases. DR-GNN tackles two key challenges: (1) adapting DRO to graph-structured data by reinterpreting GNNs as graph smoothing regularizers, and (2) addressing the sparsity of recommendation data by introducing perturbations to expand the training distribution's support. DR-GNN is implemented efficiently and effectively, with extensive experiments showing its superiority over existing methods under three types of distribution shifts: popularity shift, temporal shift, and exposure shift. Theoretical analysis confirms that DR-GNN's robustness is guaranteed when the divergence between training and testing distributions is bounded. DR-GNN outperforms other methods in performance and stability, demonstrating its effectiveness in handling distribution shifts in recommendation systems. The method is theoretically grounded and provides a new perspective for enhancing the robustness of graph-based recommendation systems.