Corruption continues to be one of the biggest societal challenges of our time. New hope is placed in Artificial Intelligence (AI) to serve as an unbiased anti-corruption agent. Ever more available (open) government data paired with unprecedented performance of such algorithms render AI the next frontier in anti-corruption. Summarizing existing efforts to use AI-based anti-corruption tools (AI-ACT), we introduce a conceptual framework to advance research and policy. It outlines why AI presents a unique tool for top-down and bottom-up anti-corruption approaches. For both approaches, we outline in detail how AI-ACT present different potentials and pitfalls for (a) input data, (b) algorithmic design, and (c) institutional implementation. Finally, we venture a look into the future and flesh out key questions that need to be addressed to develop AI-ACT while considering citizens' views, hence putting "society in the loop".