This thesis explores how AI is currently adopted in Agile software development teams within SMEs and how Responsible AI principles can be translated into practical development workflows. Using a qualitative, service design-informed approach, the study combines interviews, shadowing sessions, workshops, and surveys in collaboration with a case organization. The findings identify strong AI adoption in code generation, a need for more structured AI-supported development processes, and the importance of formal structures for guiding responsible AI use in everyday workflows. Based on the findings, the thesis proposes the RAISE Framework, a workflow-oriented framework designed to help SMEs integrate Responsible AI practices into everyday software development processes.