Sequence variation in regulatory DNA alters gene expression and shapes genetically complex traits. However, identifying individual causal regulatory variants is challenging. Here, we use a massively parallel reporter assay to measure the cis-regulatory consequences of 5,832 wild-type DNA variants on the promoters of 2,503 genes in the yeast Saccharomyces cerevisiae. We identified 451 causal variants, which underlie genetic loci known to affect gene expression. Several promoters harbored multiple causal variants. In five promoters, the variant pairs showed non-additive epistatic interactions. Causal variants were enriched for conserved nucleotides, tended to have a low frequency of derived alleles, and were depleted of promoters for essential genes, which is consistent with the action of negative selection. Causal variants were also enriched for alterations in transcription factor binding sites. Models that integrate these characteristics provided a modest but statistically significant ability to predict causal variants. This work revealed a complex molecular basis for cis-acting regulatory variation.