Graph neural networks (GNNs) have excelled in various graph learning tasks, particularly node classification. However, their performance is often hampered by noisy measurements in real-world graphs, which can corrupt critical patterns in the data. To address this, we propose a novel uncertainty-aware graph learning framework inspired by distributionally robust optimization. Specifically, we use a graph neural network-based encoder to embed the node features and find the optimal node embeddings by minimizing the worst-case risk through a minimax formulation. Such an uncertainty-aware learning process leads to improved node representations and a more robust graph predictive model that effectively mitigates the impact of uncertainty arising from data noise. Our experimental results demonstrate superior predictive performance over baselines across noisy scenarios.