Recent progress in deep learning has greatly improved the prediction of RNA splicing from DNA sequence. Here, we present Pangolin, a deep learning model to predict splice site strength in multiple tissues. Pangolin outperforms state-of-the-art methods for predicting RNA splicing on a variety of prediction tasks. Pangolin improves prediction of the impact of genetic variants on RNA splicing, including common, rare, and lineage-specific genetic variation. In addition, Pangolin identifies loss-of-function mutations with high accuracy and recall, particularly for mutations that are not missense or nonsense, demonstrating remarkable potential for identifying pathogenic variants.