Kidney disease is highly heritable; however, the causal genetic variants, the cell types in which these variants function, and the molecular mechanisms underlying kidney disease remain largely unknown. To identify genetic loci affecting kidney function, we performed a GWAS using multiple kidney function biomarkers and identified 462 loci. To begin to investigate how these loci affect kidney function, we generated single-cell chromatin accessibility (scATAC-seq) maps of the human kidney and identified candidate cis-regulatory elements (cCREs) for kidney podocytes, tubule epithelial cells, and kidney endothelial, stromal, and immune cells. Kidney tubule epithelial cCREs explained 58% of kidney function SNP-heritability and kidney podocyte cCREs explained an additional 6.5% of SNP-heritability. In contrast, little kidney function heritability was explained by kidney endothelial, stromal, or immune cell-specific cCREs. Through functionally informed fine-mapping, we identified putative causal kidney function variants and their corresponding cCREs. Using kidney scATAC-seq data, we created a deep learning model (which we named ChromKid) to predict kidney cell type-specific chromatin accessibility from sequence. ChromKid and allele specific kidney scATAC-seq revealed that many fine-mapped kidney function variants locally change chromatin accessibility in tubule epithelial cells. Enhancer assays confirmed that fine-mapped kidney function variants alter tubule epithelial regulatory element function. To map the genes which these regulatory elements control, we used CRISPR interference (CRISPRi) to target these regulatory elements in tubule epithelial cells and assessed changes in gene expression. CRISPRi of enhancers harboring kidney function variants regulated NDRG1 and RBPMS expression. Thus, inherited differences in tubule epithelial NDRG1 and RBPMS expression may predispose to kidney disease in humans. We conclude that genetic variants affecting tubule epithelial regulatory element function account for most SNP-heritability of human kidney function. This work provides an experimental approach to identify the variants, regulatory elements, and genes involved in polygenic disease.