Unsupervised domain adaptation (UDA) involves a supervised loss in a labeled source domain and an unsupervised loss in an unlabeled target domain, which often faces more severe overfitting (than classical supervised learning) as the supervised source loss has clear domain gap and the unsupervised target loss is often noisy due to the lack of annotations. This paper presents RDA, a robust domain adaptation technique that introduces adversarial attacking to mitigate overfitting in UDA. We achieve robust domain adaptation by a novel Fourier adversarial attacking (FAA) method that allows large magnitude of perturbation noises but has minimal modification of image semantics, the former is critical to the effectiveness of its generated adversarial samples due to the existence of ‘domain gaps’. Specifically, FAA decomposes images into multiple frequency components (FCs) and generates adversarial samples by just perturbating certain FCs that capture little semantic information. With FAA-generated samples, the training can continue the ‘random walk’ and drift into an area with a flat loss landscape, leading to more robust domain adaptation. Extensive experiments over multiple domain adaptation tasks show that RDA can work with different computer vision tasks with superior performance.