Neurodevelopmental impairments associated with congenital heart disease (CHD) may arise from perturbations in brain developmental pathways, including the formation of sulcal patterns. While genetic factors contribute to sulcal features, the association of noncoding variants (ncDNVs) with sulcal patterns in people with CHD remains poorly understood. Leveraging deep learning models, we examined the predicted impact of ncDNVs on gene regulatory signals. Predicted impact was compared between participants with CHD and a jointly called cohort without CHD. We then assessed the relationship of the predicted impact of ncDNVs with their sulcal folding patterns. ncDNVs predicted to increase H3K9me2 modification were associated with larger disruptions in right parietal sulcal patterns in the CHD cohort. Genes predicted to be regulated by these ncDNVs were enriched for functions related to neuronal development. This highlights the potential of deep learning models to generate hypotheses about the role of noncoding variants in brain development.