It has been hypothesised that nonsyndromic cleft lip/palate (nsCL/P) and cancer may share aetiological risk factors. Population studies have found inconsistent evidence for increased incidence of cancer in nsCL/P cases, but several genes (e.g., CDH1, AXIN2) have been implicated in the aetiologies of both phenotypes. We aimed to evaluate shared genetic aetiology between nsCL/P and oral cavity/oropharyngeal cancers (OC/OPC), which affect similar anatomical regions. Using a primary sample of 5,048 OC/OPC cases and 5,450 controls of European ancestry and a replication sample of 750 cases and 336,319 controls from UK Biobank, we estimate genetic overlap using nsCL/P polygenic risk scores (PRS) with Mendelian randomization analyses performed to evaluate potential causal mechanisms. In the primary sample, we found strong evidence for an association between a nsCL/P PRS and increased odds of OC/OPC (per standard deviation increase in score, odds ratio [OR]: 1.09; 95% confidence interval [CI]: 1.04, 1.13; p = .000053). Although confidence intervals overlapped with the primary estimate, we did not find confirmatory evidence of an association between the PRS and OC/OPC in UK Biobank (OR 1.02; 95% CI: 0.95, 1.10; p = .55). Mendelian randomization analyses provided evidence that major nsCL/P risk variants are unlikely to influence OC/OPC. Our findings suggest possible shared genetic influences on nsCL/P and OC/OPC. © 2020 The Authors. Genetic Epidemiology published by Wiley Periodicals LLC.