This chapter examines the application of Corporate Digital Responsibility (CDR) principle to the implementation of AI governance frameworks. With the introduction of the EU AI Act, organizations face new regulatory demands that classic IT governance cannot fully address, especially regarding AI-specific risks and ethical considerations. The chapter argues that effective AI governance must go beyond compliance, embedding principles such as transparency, fairness, privacy, accountability, sustainability, and stakeholder engagement into organizational processes. It highlights the challenges of translating high-level ethical values into actionable requirements, particularly in fast-paced, resource-constrained environments. The authors emphasize the importance of cross-functional collaboration, continuous AI literacy training, and the allocation of clear responsibilities to ensure responsible AI development and deployment. By leveraging existing governance structures and fostering a culture of ethical reflection, organizations can better manage the risks and societal impacts of AI. Ultimately, the chapter demonstrates that CDR provides a comprehensive foundation for responsible AI governance, enabling organizations to align innovation with ethical standards and societal expectations in an evolving regulatory landscape.