Collaborative filtering (CF) is a central solution for capturing various user-item relationships in building recommender systems. However, when the relationships are sparsely observed, it is challenging to obtain enough signals to infer precise user preferences. Recent studies have attempted to address the sparsity issue by incorporating multimodal information (e.g., image and text) into CF models. However, existing methods mainly focus on capturing modal-specific user preference with multiple unimodal graphs, ignoring the complex nature of user behavior, which is determined by an intricate fusion of multimodal information. Therefore, we develop a Self-supervised Multimodal Graph Convolutional Network (SMGCN), which aims to learn the cross-modal user preferences over multiple modalities with an expressive multimodal fusion on a single graph.More importantly, to facilitate and enhance multimodal fusion in SMGCN, we devise two novel self-supervised learning techniques. 1) Collaborative Multimodal Alignment (CMA) uses contrastive learning to align the domain-specific multimodal semantics with the user-item relational semantics. 2) Multimodal Consistency Regularization (MCR) alleviates the sensitivity on a certain modality and increases model robustness. The experimental results demonstrate that our model consistently outperforms advanced multimodal models on three benchmark datasets.