Understanding the function of rare non-coding variants represents a significant challenge. Using MapUTR, a screening method, we studied the function of rare 3′ UTR variants affecting mRNA abundance post-transcriptionally. Among 17,301 rare gnomAD variants, an average of 24.5% were functional, with 70% in cancer-related genes, many in critical cancer pathways. This observation motivated an interrogation of 11,929 somatic mutations, uncovering 3928 (33%) functional mutations in 155 cancer driver genes. Functional MapUTR variants were enriched in microRNA- or protein-binding sites and may underlie outlier gene expression in tumors. Further, we introduce untranslated tumor mutational burden (uTMB), a metric reflecting the amount of somatic functional MapUTR variants of a tumor and show its potential in predicting patient survival. Through prime editing, we characterized three variants in cancer-relevant genes (MFN2, FOSL2, and IRAK1), demonstrating their cancer-driving potential. Our study elucidates the function of tens of thousands of non-coding variants, nominates non-coding cancer driver mutations, and demonstrates their potential contributions to cancer.