Artificial Intelligence (AI) increasingly becomes an indispensable advisor. New ethical concerns arise if AI persuades people to behave dishonestly. In an experiment, we study how AI advice (generated by a Natural-Language-processing algorithm) affects (dis)honesty, compare it to equivalent human advice, and test whether transparency about advice source matters. We find that dishonesty-promoting advice increases dishonesty, whereas honesty-promoting advice does not increase honesty. This is the case for both AI and human advice. Algorithmic transparency, a commonly proposed policy to mitigate AI risks, does not affect behaviour. The findings mark the first steps towards managing AI advice responsibly.