Several studies profile similar single cell RNA-Seq (scRNA-Seq) data using different technologies and platforms. A number of alignment methods have been developed to enable the integration and comparison of scRNA-Seq data from such studies. While each performs well on some of the datasets, to date no method was able to both perform the alignment using the original expression space and generalize to new data. To enable such analysis we developed Single Cell Iterative Point set Registration (SCIPR) which extends methods that were successfully applied to align image data to scRNA-Seq. We discuss the required changes needed, the resulting optimization function, and algorithms for learning a transformation function for aligning data. We tested SCIPR on several scRNA-Seq datasets. As we show it successfully aligns data from several different cell types, improving upon prior methods proposed for this task. In addition, we show the parameters learned by SCIPR can be used to align data not used in the training and to identify key cell type-specific genes.