Requirements Engineering (RE) is the discipline for identifying, analyzing, as well as ensuring the implementation and delivery of user, technical, and societal requirements. Recently reported issues concerning the acceptance of Artificial Intelligence (AI) solutions after deployment, e.g. in the medical, automotive, or scientific domains, stress the importance of RE for designing and delivering Responsible AI systems. In this paper, we argue that RE should not only be carefully conducted but also tailored for Responsible AI. We outline related challenges for research and practice.