Graph neural networks (GNNs) have shown great ability for node classification on graphs. However, the success of GNNs relies on abundant labeled data, while obtaining high-quality labels is costly and challenging, especially for newly emerging domains. Hence, unsupervised domain adaptation (UDA), which trains a classifier on the labeled source graph and adapts it to the unlabeled target graph, is attracting increasing attention. Various approaches have been proposed to alleviate the distribution shift between the source and target graphs to facilitate the classifier adaptation. However, most of them simply adopt existing UDA techniques developed for independent and identically distributed data to gain domain-invariant node embeddings for graphs, which do not fully consider the graph structure and message-passing mechanism of GNNs during the adaptation and will fail when label distribution shift exists among domains. In this paper, we proposed a novel framework that adopts link prediction to connect nodes between source and target graphs, which can facilitate message-passing between the source and target graphs and augment the target nodes to have ``in-distribution'' neighborhoods with the source domain. This strategy modified the target graph on the input level to reduce its deviation from the source domain in the embedding space and is insensitive to disproportional label distributions across domains. To prevent the loss of discriminative information in the target graph, we further design a novel identity-preserving learning objective, which guides the learning of the edge insertion module together with reconstruction and adaptation losses. Experimental results on real-world datasets demonstrate the effectiveness of our framework.