Artificial Intelligence (AI) technologies undergo rapidly increasing integration in all areas of everyday life, including healthcare, employment, and public services. To reconcile abstract theoretical concepts with the practical realities of AI development and deployment in the public sector, this study formulates Human-Centered AI (HCAI) design principles, recognizing the unique aspects of the public sector. The study argues for bespoke AI design and implementation strategies that prioritize societal needs over commercial interests and incorporate citizen perspectives into the design principles. The study employs Action Design Research and draws from Social Contract Theory, aiming to advance the dialogue on responsible AI practices within the public sector. These principles offer valuable insights for both academics and practitioners, bridging the gap between theory and practice, enriching the information systems discipline, and fostering a deeper understanding of a socially responsible AI design and deployment in public services.