We propose that digital technologies and related data become increasingly prevalent and that, consequently, ethical concerns arise. Looking at four principal stakeholders, we propose corporate digital responsibility (CDR) as a novel concept. We define CDR as the set of shared values and norms guiding an organization's operations with respect to four main processes related to digital technology and data. These processes are the creation of technology and data capture, operation and decision making, inspection and impact assessment, and refinement of technology and data. We expand our discussion by highlighting how to managerially effectuate CDR compliant behavior based on an organizational culture perspective. Our conceptualization unlocks future research opportunities, especially regarding pertinent antecedents and consequences. Managerially, we shed first light on how an organization's shared values and norms regarding CDR can get translated into actionable guidelines for users. This provides grounds for future discussions related to CDR readiness, implementation, and success.