Single-cell RNA sequencing provides high-throughput gene expression information and offers higher resolution of cell differences compared to bulk RNA sequencing, which helps identify cell types and explore cellular heterogeneity at the single-cell level. Although many single-cell clustering methods based on masked autoencoders have been developed recently, they rarely effectively utilize the correlations between cells, resulting in suboptimal clustering results. In this work, we propose a novel clustering method for scRNA-seq data based on a masked graph convolutional autoencoder, which incorporates a graph convolutional network onto the basis of a masked autoencoder to enhance the capture of the correlation between cells and genes by fusing the cell-cell interaction graph and the gene expression matrix. By increasing the relationships between cells, dimensionality reduction is guided, and a clustering-friendly representation is obtained. We conducted extensive comparative experiments using various clustering evaluation metrics on six scRNA-seq datasets from different sequencing platforms. The experimental results demonstrate that scMGCAE outperforms other methods on these datasets.