This commentary looks at the use of corporate social responsibility (CSR) mechanisms for implementing responsible data use. The commentary offers an overview of CSR theory and the discourse on a growing phenomenon known as corporate digital responsibility (CDR). The commentary links these theories to the historical debates on the nature of technology, ethics, and society. The aim is to reflect on CSR and CDR mechanisms and ignite the discussion on their adequacy considering the pursuit of data responsibility. Through our discussion and brief case studies, the paper reveals the gaps in relying on CSR and CDR and the need for a broader societal and comprehensive approach.