Artificial Intelligence (AI) is arguably one of the most powerful and disruptive technologies of our times which may pose challenges as well as opportunities to contemporary political organizations. Studying AI from a lens of perceived uncertainty, this article studies the policy response of the European Commission toward this fast-paced emerging technology. By empirically focusing on the Commission's policy process from start to end, from initial communication to concrete proposal, the article shows how different types of narratives are used to construct the new policy area of AI policy. A novel theoretical framework is constructed building on a combination of narrative organizational studies and narrative policy studies, displaying how narratives play a key role in organizational sensemaking, agency construction and anchoring. The paper finds that the Commission broadly makes sense of AI technologies with a future-oriented discourse, establishes agency to existing and new forms of political organizing and anchors the policy response within the overarching frame of the EU single market policy. The main contribution of the paper is that it shows how political organizations settles uncertainty through narratives and sketches a way forward through establishing policy goals and anchoring them within pre-existing lines of political mobilization.