We investigate whether and how AI-powered algorithms can serve as moral advisors. In a series of online studies, we measure participants' propensity to choose between a more and a less ethical alternative in various scenarios (recruitment process, organ donation, criminal prosecution). Before making their decision, participants receive advice from a moral advisor who declares the unethical alternative to be either acceptable or unacceptable. We manipulate whether the advisor is human or an AI-based algorithm, as well as the information about the characteristics and/or functioning of the advisor. Our results show that advice from AI-based advisors is readily heeded to a comparable extent as advice from human moral advisors. The influence of moral advice seems to be quite robust to the specific configurations of the AI-based advisor. Interestingly, our participants even ignore information that clearly disqualifies the advisor when the advisor is an AI-powered algorithm, but not when the advisor is human.