In recent years, federated self-supervised learning has achieved great progress in the natural language processing and computer vision community. However, little work is exploring self-supervised federated settings on single-cell data, especially on scRNA-seq datasets across various cells. Although one previous work named contrastive-sc on self-supervised single-cell clustering of independently and identically distributed (IID) scRNA-seq data is based on SimCLR-style contrastive learning model, they cannot leverage decentralized unlabeled scRNA-seq data to learn a generic representation with preserving data privacy. To bridge this gap, we introduce a new non-IID scRNA-seq benchmark for federated self-supervised learning to perform single-cell clustering. Furthermore, we propose a novel federated self-supervised learning framework for single-cell clustering, namely FedSC, that can leverage unlabeled data from multiple sequencing platforms to learn scRNA- seq representations while preserving data privacy. We conduct extensive experiments on PBMC & Mouse bladder cells under both IID and non-IID settings. The experimental results demonstrate the effectiveness of our proposed FedSC in federated self-supervised clustering of scRNA-seq data.