Obstructive sleep apnea (OSA) is characterized by decreased breathing events that occur through the night, with severity reported as the apnea-hypopnea index (AHI), which is associated with certain craniofacial features. In this study, we used data from 1366 patients collected as part of Stanford Technology Analytics and Genomics in Sleep (STAGES) across 11 US and Canadian sleep clinics and analyzed 3D craniofacial scans with the goal of predicting AHI, as measured using gold standard nocturnal polysomnography (PSG). First, the algorithm detects pre-specified landmarks on mesh objects and aligns scans in 3D space. Subsequently, 2D images and depth maps are generated by rendering and rotating scans by 45-degree increments. Resulting images were stacked as channels and used as input to multi-view convolutional neural networks, which were trained and validated in a supervised manner to predict AHI values derived from PSGs. The proposed model achieved a mean absolute error of 11.38 events/hour, a Pearson correlation coefficient of 0.4, and accuracy for predicting OSA of 67% using 10-fold cross-validation. The model improved further by adding patient demographics and variables from questionnaires. We also show that the model performed at the level of three sleep medicine specialists, who used clinical experience to predict AHI based on 3D scan displays. Finally, we created topographic displays of the most important facial features used by the model to predict AHI, showing importance of the neck and chin area. The proposed algorithm has potential to serve as an inexpensive and efficient screening tool for individuals with suspected OSA.