Anchor Link Prediction (ALP) across social networks plays a pivotal role in inter-network applications. The difficulty of anchor link prediction across social networks lies in how to consider the factors affecting nodes alignment comprehensively. In recent years, predicting anchor links based on network embedding has become the main trend. For social networks, previous anchor link prediction methods first integrate neighbourhood nodes associated with a user node to obtain a fusion embedding vector from global perspective, and then predict anchor links based on the similarity between fusion vectors corresponding with different user nodes. However, the social network structure contains a lot of structural noise, which is ignored by the fusion vector. To address the challenge, we propose a novel structure-noise-aware anchor link prediction framework across social networks (SNALP), which models all the edges of the node from a fine-grained perspective and evaluates the contribution of them. Then, each edge is given a different weight according to their contribution. While the trusted edges are enhanced, the effects of noisy edges are reduced. SNALP can solve the network embedding and structure-noise-aware alignment under a unified optimization framework. Extensive experiments on real social network datasets demonstrate the effectiveness and efficiency of the proposed approach compared with several state-of-the-art methods.