International Digital Cooperation must be underpinned by the effective international governance of artificial intelligence (AI). AI systems pose numerous transboundary policy problems in both the short- and the longterm. The international governance of AI should be anchored to a regime under the UN which is inclusive (of multiple stakeholders), anticipatory (of fast-progressing AI technologies and impacts), responsive (to the rapidly evolving technology and its uses) and reflexive (critically reviews and updates its policy principles). We propose some options for the international governance of AI which could help coordinate existing international law on AI, forecast future developments, risks and opportunities, and fill critical gaps in international governance.