Peer review is a necessary and essential quality control step for scientific publications but lacks proper incentives. Indeed, the process, which is very costly in terms of time and intellectual investment, not only is not remunerated by the journals but it is also not openly recognized by the academic community as a relevant scientific output for a researcher. Therefore, scientific dissemination is affected in timeliness, quality and fairness. Here, to solve this issue, we propose a blockchain-based incentive system that rewards scientists for peer reviewing other scientists’ work and that builds up trust and reputation. We designed a privacy-oriented protocol of smart contracts called Ants-Review that allows authors to issue a bounty for open anonymous peer reviews on Ethereum. If requirements are met, peer reviews will be accepted and paid by the approver proportionally to their assessed quality. To promote ethical behaviour and inclusiveness the system implements a gamified mechanism that allows the whole community to evaluate the peer reviews and vote for the best ones.