Single-cell RNA sequencing (scRNA-seq) has provided a large volume of data to discover cellular differences. Unsupervised clustering of scRNA-seq data is an important analytical method to identify cell subtypes. This paper introduces scGECA, a graph embedded representation learning method for clustering, which learns a low-dimensional data representation through an optimized graph attention network and uses a multilayer perceptron as a decoder to optimize the graph aggregation representation. As a result, we obtain a low-dimensional feature that is more suitable for single-cell clustering. Extensive experiments on multiple real-world datasets demonstrate that scGECA outperforms other state-of-the-art single-cell clustering methods in both clustering accuracy and robustness.