This paper proposes a methodological redirection of the philosophical debate on artificial moral agency (AMA) in view of increasingly pressing practical needs due to technological development. This “normative approach” suggests abandoning theoretical discussions about what conditions may hold for moral agency and to what extent these may be met by artificial entities such as AI systems and robots. Instead, the debate should focus on how and to what extent such entities should be included in human practices normally assuming moral agency and responsibility of participants. The proposal is backed up by an analysis of the AMA debate, which is found to be overly caught in the opposition between so-called standard and functionalist conceptions of moral agency, conceptually confused and practically inert. Additionally, we outline some main themes of research in need of attention in light of the suggested normative approach to AMA.