This article proposes the techno-cultural workshop as an innovative method for opening up the materiality of computational media and data flows and order to increase understanding of the socio-cultural and political-economic dimensions of datafication. Building upon the critical, creative hacker ethos of technological engagement, and the collective practice of the hackathon, the techno-cultural workshops is directed at humanities researchers and social and cultural theorists. We conceptually frame this method via Simondon as a practice-led opportunity to rethink the contested relationship between the human, nature and technology, with a view to challenging social and cultural theory that ignores the human reality of the technical object. We outline an exemplar techno-cultural workshop which explored mobile apps as i) an opportunity to use new digital tools for empirical research, and ii) as technical objects and elements for better understanding their social and cultural dimensions. We see political efficacy in the techno-cultural method not only in augmenting critical and creative agency, but as a practical exploration of the concept of data technicity, an inexhaustible relationality that exceeds the normative and regulatory utility of the data we generate and can be linked anew into collective capacities to act.