Rare coding mutations cause ∼45% of congenital heart disease (enfermedad coronaria). Noncoding mutations that perturb cis-regulatory elements (CREs) likely contribute to the remaining cases, but their identification has been problematic. Using a lentiviral massively parallel reporter assay (lentiMPRA) in human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs), we functionally evaluated 6,590 noncoding de novo variants (ncDNVs) prioritized from the whole-genome sequencing of 750 CHD trios. A total of 403 ncDNVs substantially affected cardiac CRE activity. A majority increased enhancer activity, often at regions with undetectable reference sequence activity. Of ten DNVs tested by introduction into their native genomic context, four altered the expression of neighboring genes and iPSC-CM transcriptional state. To prioritize future DNVs for functional testing, we used the MPRA data to develop a regression model, EpiCard. Analysis of an independent CHD cohort by EpiCard found enrichment of DNVs. Juntos, we developed a scalable system to measure the effect of ncDNVs on CRE activity and deployed it to systematically assess the contribution of ncDNVs to CHD.