Exact inference in Bayesian networks is NP-Hard. While many parallel algorithms have been proposed for this irregular problem, none have been shown to scale to even hundreds of processors. In this paper, we present a scalable distributed-memory parallel algorithm for exact inference based on Darwiche's approach, which poses inference as upward and downward accumulation of values computed at the nodes of an arithmetic circuit, a rooted directed acyclic graph. Our work includes parallel algorithms for both construction of the arithmetic circuit as well as inference using the circuit. We demonstrate the scalability of our algorithms for up to 1,536 cores on synthetic as well as real datasets, whose corresponding arithmetic circuits contain up to billions of nodes. The runtime for inference is only a small fraction of the runtime for circuit construction, providing the ability to quickly perform multiple inferences once the circuit is constructed.