Previous studies have shown that copy-number variants (CNVs) contribute to the risk of complex developmental phenotypes. However, the contribution of global CNV burden to the risk of sporadic congenital heart disease (CHD) remains incompletely defined. We generated genome-wide CNV data by using Illumina 660W-Quad SNP arrays in 2,256 individuals with CHD, 283 trio CHD-affected families, and 1,538 controls. We found association of rare genic deletions with CHD risk (odds ratio [OR] = 1.8, p = 0.0008). Rare deletions in study participants with CHD had higher gene content (p = 0.001) with higher haploinsufficiency scores (p = 0.03) than they did in controls, and they were enriched with Wnt-signaling genes (p = 1 × 10−5). Recurrent 15q11.2 deletions were associated with CHD risk (OR = 8.2, p = 0.02). Rare de novo CNVs were observed in ∼5% of CHD trios; 10 out of 11 occurred on the paternally transmitted chromosome (p = 0.01). Some of the rare de novo CNVs spanned genes known to be involved in heart development (e.g., HAND2 and GJA5). Rare genic deletions contribute ∼4% of the population-attributable risk of sporadic CHD. Second to previously described CNVs at 1q21.1, deletions at 15q11.2 and those implicating Wnt signaling are the most significant contributors to the risk of sporadic CHD. Rare de novo CNVs identified in CHD trios exhibit paternal origin bias.