Genome-wide association studies for non-syndromic orofacial clefting (OFC) have identified single nucleotide polymorphisms (SNPs) at loci where the presumed risk-relevant gene is expressed in oral periderm. The functional subsets of such SNPs are difficult to predict because the sequence underpinnings of periderm enhancers are unknown. We applied ATAC-seq to models of human palate periderm, including zebrafish periderm, mouse embryonic palate epithelia, and a human oral epithelium cell line, and to complementary mesenchymal cell types. We identified sets of enhancers specific to the epithelial cells and trained gapped-kmer support-vector-machine classifiers on these sets. We used the classifiers to predict the effects of 14 OFC-associated SNPs at 12q13 near KRT18. All the classifiers picked the same SNP as having the strongest effect, but the significance was highest with the classifier trained on zebrafish periderm. Reporter and deletion analyses support this SNP as lying within a periderm enhancer regulating KRT18/KRT8 expression.