Gene selection in unannotated large single cell RNA sequencing (scRNA-seq) data is important and crucial step in the preliminary step of downstream analysis. The existing approaches are primarily based on high variation (highly variable genes) or significant high expression (highly expressed genes) failed to provide stable and predictive feature set due to technical noise present in the data. Here, we propose RgCop, a novel regularized copula based method for gene selection from large single cell RNA-seq data. RgCop utilizes copula correlation (Ccor), a robust equitable dependence measure that captures multivariate dependency among a set of genes in single cell expression data. We formulate an objective function by adding l1 regularization term with Ccor to penalizes the redundant co-efficient of features/genes, resulting non-redundant effective features/genes set. Results show a significant improvement in the clustering/classification performance of real life scRNA-seq data over the other state-of-the-art. RgCop performs extremely well in capturing dependence among the features of noisy data due to the scale invariant property of copula, thereby improving the stability of the method. Moreover, the differentially expressed (DE) genes identified from the clusters of scRNA-seq data are found to provide an accurate annotation of cells. Finally, the features/genes obtained from RgCop is able to annotate the unknown cells with high accuracy.