Developing efficient and scalable algorithms for Latent Dirichlet Allocation (LDA) is of wide interest for many applications. Previous work has developed an O(1) Metropolis-Hastings sampling method for each token. However, the performance is far from being optimal due to random accesses to the parameter matrices and frequent cache misses. In this paper, we first carefully analyze the memory access efficiency of existing algorithms for LDA by the scope of random access, which is the size of the memory region in which random accesses fall, within a short period of time. We then develop WarpLDA, an LDA sampler which achieves both the best O(1) time complexity per token and the best O(K) scope of random access. Our empirical results in a wide range of testing conditions demonstrate that WarpLDA is consistently 5-15x faster than the state-of-the-art Metropolis-Hastings based LightLDA, and is comparable or faster than the sparsity aware F+LDA. With WarpLDA, users can learn up to one million topics from hundreds of millions of documents in a few hours, at an unprecedentedly throughput of 11G tokens per second.