Single-cell RNA sequencing is an emerging technique in the field of biology that departs radically from the previous assumption of gene-expression homogeneity within a tissue. The large quantity of data generated by this technology enables discoveries of cellular biology and disease mechanics that were previously not possible, and calls for accurate, scalable, and efficient processing pipelines. In this work, we propose SSCAE (spiking single-cell autoencoder), a novel SNN-based autoencoder for sc-RNA-seq dimensionality reduction. We apply this architecture to a variety of datasets, and the results show that it can match and surpass the performance of current state-of-the-art techniques. Moreover, the potential of this technique lies in its ability to be scaled up and to take advantage of neuromorphic hardware, circumventing the memory bottleneck that currently limits the size of sequencing datasets that can be processed.