For AI technology to fulfill its full promises, we must design effective mechanisms into the AI systems to support responsible AI behavior and curtail potential irresponsible use, e.g. in areas of privacy protection, human autonomy, robustness, and prevention of biases and discrimination in automated decision making. In this paper, we present a framework that provides computational facilities for parties in a social ecosystem to produce the desired responsible AI behaviors. To achieve this goal, we analyze AI systems at the architecture level and propose two decentralized cryptographic mechanisms for an AI system architecture: (1) using Autonomous Identity to empower human users, and (2) automating rules and adopting conventions within social institutions. We then propose a decentralized approach and outline the key concepts and mechanisms based on Decentralized Identifier (DID) and Verifiable Credentials (VC) for a general-purpose computational infrastructure to realize these mechanisms. We argue the case that a decentralized approach is the most promising path towards Responsible AI from both the computer science and social science perspectives.