Data scarcity, e.g., labeled data being either unavailable or too expensive, is a perpetual challenge of recommendation systems. Cross-domain recommendation leverages the label information in the source domain to facilitate the task in the target domain. However, in many real-world cross-domain recommendation systems, the source domain and the target domain are sampled from different data distributions, which obstructs the cross-domain knowledge transfer. In this paper, we propose to specifically align the data distributions between the source domain and the target domain to alleviate imbalanced sample distribution and thus challenge the data scarcity issue in the target domain. Technically, our proposed approach builds an adversarial adaptation (AA) framework to adversarially train the target model together with a pre-trained source model. A domain discriminator plays the two-player minmax game with the target model and guides the target model to learn domain-invariant features that can be transferred across domains. At the same time, the target model is calibrated to learn domain-specific information of the target domain. With such a formulation, the target model not only learns domain-invariant features for knowledge transfer, but also preserves domain-specific information for target recommendation. We apply the proposed method to address the issues of insufficient data and imbalanced sample distribution in real-world Click-Through Rate (CTR)/Conversion Rate (CVR) predictions on a large-scale dataset. Specifically, we formulate our approach as a plug-and-play module to boost existing recommendation systems. Extensive experiments verify that the proposed method is able to significantly improve the prediction performance on the target domain. For instance, our method can boost PLE with a performance improvement of 13.88% in terms of Area Under Curve (AUC) compared with single-domain PLE.