Nowadays, it is common for one natural person to join multiple social networks to enjoy different kinds of services. Linking identical users across multiple social networks, also known as social network alignment, is an important problem of great research challenges. Existing methods usually link social identities on the pairwise sample level, which may lead to undesirable performance when the number of available annotations is limited. Motivated by the isomorphism information, in this paper we consider all the identities in a social network as a whole and perform social network alignment from the distribution level. The insight is that we aim to learn a projection function to not only minimize the distance between the distributions of user identities in two social networks, but also incorporate the available annotations as the learning guidance. We propose three models SNNAu, SNNAb and SNNAo to learn the projection function under the weakly-supervised adversarial learning framework. Empirically, we evaluate the proposed models over multiple datasets, and the results demonstrate the superiority of our proposals.