Public and private organizations increasingly deploy AI-systems for the autonomous execution of tasks and decisions. Given these systems’ inherent complexity, even the strictest safety measures cannot fully prevent adverse outcomes, subjecting individuals to serious harm. This raises the following question: Who ought to take responsibility for AI-related harm, when it is not the direct result of human fault? Drawing on the philosophy of tort law, I argue that AI-deployers have a strict moral duty to take responsibility for harmful outcomes, even if the deployment of the harm-imposing AI is morally permissible. In contrast to traditional responsibility accounts based on blameworthiness, the proposed account of strict responsibility is not predicated on a prior duty violation but on a proactive duty to provide redress in case individuals are harmed. It is a relational duty that arises from what I call the “accidental relationship”, which highlights the intrinsic connection between AI-deployers and the harmed individuals, and in which taking responsibility is an expression of recognizing the harmed individual as moral equal.