Dynamic control flow is an important technique often used to design expressive and efficient deep learning computations for applications such as text parsing, machine translation, exiting early out of deep models and so on. However, the resulting control flow divergence makes batching, an important performance optimization, difficult to perform manually. In this paper, we present ACRoBat, a framework that enables efficient automatic batching for dynamic deep learning computations by performing hybrid static+dynamic compiler optimizations and end-to-end tensor code generation. ACRoBat performs up to 8.5 better than DyNet, a state-of-the-art framework for automatic batching, on an Nvidia GeForce RTX 3070 GPU.