Stance detection aims at identifying people's stand-point towards a given target. New targets are constantly appearing on social media, making previous annotated data unusable by stance detection models relying on classical supervised machine learning. Thus, cross-target stance detection which uses labeled data from source targets to learn a model that can be adapted to the destination new target, has become a prevailing research direction. However, previous methods rely on manually chosen similar source-destination target pairs and lack generalization to unseen targets with no explicit relation to known ones. To this end, we investigate the problem from a domain adaptation perspective and further propose a novel Unified Target-aware Domain Adaptation method (UTDA) that leverages knowledge transfer capability of transformer-based language model. The proposed method can effectively extract critical target-shared features for detecting stance by feature disentanglement and automatically learn to identify target relations. UTDA can easily be applied to a new unseen target since it does not rely on any pre-defined target pairs. Experimental results on two benchmark stance datasets demonstrate that our method achieves better performance than strong baselines