Quantification of gene expression levels at the single cell level has revealed that gene expression can vary substantially even across a population of homogeneous cells. However, it is currently unclear what genomic features control variation in gene expression levels, and whether common genetic variants may impact gene expression variation. Here, we take a genome-wide approach to identify expression variance quantitative trait loci (vQTLs). To this end, we generated single cell RNA-seq (scRNA-seq) data from induced pluripotent stem cells (iPSCs) derived from 53 Yoruba individuals. We collected data for a median of 95 cells per individual and a total of 5,447 single cells, and identified 235 mean expression QTLs (eQTLs) at 10% FDR, of which 79% replicate in bulk RNA-seq data from the same individuals. We further identified 5 vQTLs at 10% FDR, but demonstrate that these can also be explained as effects on mean expression. Our study suggests that dispersion QTLs (dQTLs) which could alter the variance of expression independently of the mean can have larger fold changes, but explain less phenotypic variance than eQTLs. We estimate 4,015 individuals as a lower bound to achieve 80% power to detect the strongest dQTLs in iPSCs. These results will guide the design of future studies on understanding the genetic control of gene expression variance.