The ideal of unfettered data circulation has fallen into crisis. As of today, a growing number of actors are introducing measures to ensure a greater degree of control over the global data pipeline. Combining critical data studies and political theory, this article conceptualises the current technopolitical conjuncture as one of ‘planetary data turbulence’ in which divergences regarding the production and circulation of data have become the norm. The concept of data turbulence emerges from studies on data friction, but this article contends that the current state of affairs requires expanding the emphasis on technosciences and materiality in these works. Drawing on Ernesto Laclau and Chantal Mouffe, the article shows that attending to antagonism and discourse makes it possible to account for the eminently political forces shaping the circulation of data. The strengths of this framework are illustrated by looking at the articulation of digital sovereignty in different geographies.