Unsupervised domain adaptation (UDA) aims to adapt models learned from a well-annotated source domain to a target domain, where only unlabeled samples are given. Current UDA approaches learn domain-invariant features by aligning source and target feature spaces through statistical discrepancy minimization or adversarial training. However, these constraints could lead to the distortion of semantic feature structures and loss of class discriminability. In this article, we introduce a novel prompt learning paradigm for UDA, named domain adaptation via prompt learning (DAPrompt). In contrast to prior works, our approach learns the underlying label distribution for target domain rather than aligning domains. The main idea is to embed domain information into prompts, a form of representation generated from natural language, which is then used to perform classification. This domain information is shared only by images from the same domain, thereby dynamically adapting the classifier according to each domain. By adopting this paradigm, we show that our model not only outperforms previous methods on several cross-domain benchmarks but also is very efficient to train and easy to implement.