Social network alignment, which aims to uncover the correspondence across different social networks, shows fundamental importance in a wide spectrum of applications such as cross-domain recommendation and information propagation. In the literature, the vast majority of the existing studies focus on the social network alignment at user level. In practice, the user-level alignment usually relies on abundant personal information and high-quality supervision, which is expensive and even impossible in the real-world scenario. Alternatively, we propose to study the problem of social group alignment across different social networks, focusing on the interests of social groups rather than personal information. However, social group alignment is non-trivial and faces significant challenges in both (i) feature inconsistency across different social networks and (ii) group discovery within a social network. To bridge this gap, we present a novel GroupAligner , a deep reinforcement learning with domain adaptation for social group alignment. In GroupAligner , to address the first issue, we propose the cycle domain adaptation approach with the Wasserstein distance to transfer the knowledge from the source social network, aligning the feature space of social networks in the distribution level. To address the second issue, we model the group discovery as a sequential decision process with reinforcement learning in which the policy is parameterized by a proposed p roximity-enhanced G raph N eural N etwork (pGNN) and a GNN-based discriminator to score the reward. Finally, we utilize pre-training and teacher forcing to stabilize the learning process of GroupAligner . Extensive experiments on several real-world datasets are conducted to evaluate GroupAligner , and experimental results show that GroupAligner outperforms the alternative methods for social group alignment.