In many real-world applications, ensuring the robustness and stability of deep neural networks (DNNs) is crucial, particularly for image classification tasks that encounter various input perturbations. While data augmentation techniques have been widely adopted to enhance the resilience of a trained model against such perturbations, there remains significant room for improvement in robustness against corrupted data and adversarial attacks simultaneously. To address this challenge, we introduce DRO-Augment, a novel framework that integrates Wasserstein Distributionally Robust Optimization (W-DRO) with various data augmentation strategies to improve the robustness of the models significantly across a broad spectrum of corruptions. Our method outperforms existing augmentation methods under severe data perturbations and adversarial attack scenarios while maintaining the accuracy on the clean datasets on a range of benchmark datasets, including but not limited to CIFAR-10-C, CIFAR-100-C, MNIST, and Fashion-MNIST. On the theoretical side, we establish novel generalization error bounds for neural networks trained using a computationally efficient, variation-regularized loss function closely related to the W-DRO problem.