Unsupervised Domain Adaptation (UDA) methods aim to transfer knowledge from a labeled source domain to an unlabeled target domain. UDA has been extensively studied in the computer vision literature. Deep networks have been shown to be vulnerable to adversarial attacks. However, very little focus is devoted to improving the adversarial robustness of deep UDA models, causing serious concerns about model reliability. Adversarial Training (AT) has been considered to be the most successful adversarial defense approach. Nevertheless, conventional AT requires ground-truth labels to generate adversarial examples and train models, which limits its effectiveness in the unlabeled target domain. In this paper, we aim to explore AT to robustify UDA models: How to enhance the unlabeled data robustness via AT while learning domain-invariant features for UDA? To answer this, we provide a systematic study into multiple AT variants that potentially apply to UDA. Moreover, we propose a novel Adversarially Robust Training method for UDA accordingly, referred to as ARTUDA. Extensive experiments on multiple attacks and benchmarks show that ARTUDA consistently improves the adversarial robustness of UDA models.