With burgeoning human disease genetic associations and single-cell genomic atlases covering a range of tissues, there are unprecedented opportunities to systematically gain insights into the mechanisms of disease-causal variation. However, sparsity and noise, particularly in the context of single-cell epigenomic data, hamper the identification of disease- or trait-relevant cell types, states, and trajectories. To overcome these challenges, we have developed the SCAVENGE method, which maps causal variants to their relevant cellular context at single-cell resolution by employing the strategy of network propagation. We demonstrate how SCAVENGE can help identify key biological mechanisms underlying human genetic variation including enrichment of blood traits at distinct stages of human hematopoiesis, defining monocyte subsets that increase the risk for severe coronavirus disease 2019 (COVID-19), and identifying intermediate lymphocyte developmental states that are critical for predisposition to acute leukemia. Our approach not only provides a framework for enabling variant-to-function insights at single-cell resolution, but also suggests a more general strategy for maximizing the inferences that can be made using single-cell genomic data.