Over 500 genetic loci have been associated with risk of cardiovascular diseases (CVDs); however, most loci are located in gene-distal non-coding regions and their target genes are not known. Here, we generated high-resolution promoter capture Hi-C (PCHi-C) maps in human induced pluripotent stem cells (iPSCs) and iPSC-derived cardiomyocytes (CMs) to provide a resource for identifying and prioritizing the functional targets of CVD associations. We validate these maps by demonstrating that promoters preferentially contact distal sequences enriched for tissue-specific transcription factor motifs and are enriched for chromatin marks that correlate with dynamic changes in gene expression. Using the CM PCHi-C map, we linked 1999 CVD-associated SNPs to 347 target genes. Remarkably, more than 90% of SNP-target gene interactions did not involve the nearest gene, while 40% of SNPs interacted with at least two genes, demonstrating the importance of considering long-range chromatin interactions when interpreting functional targets of disease loci.