Responsible prompt engineering has emerged as a critical framework for ensuring that generative artificial intelligence (AI) systems serve society's needs while minimizing potential harms. As generative AI applications become increasingly powerful and ubiquitous, the way we instruct and interact with them through prompts has profound implications for fairness, accountability, and transparency. This article examines how strategic prompt engineering can embed ethical and legal considerations and societal values directly into AI interactions, moving beyond mere technical optimization for functionality. This article proposes a comprehensive framework for responsible prompt engineering that encompasses five interconnected components: prompt design, system selection, system configuration, performance evaluation, and prompt management. Drawing from empirical evidence, the paper demonstrates how each component can be leveraged to promote improved societal outcomes while mitigating potential risks. The analysis reveals that effective prompt engineering requires a delicate balance between technical precision and ethical consciousness, combining the systematic rigor and focus on functionality with the nuanced understanding of social impact. Through examination of real-world and emerging practices, the article illustrates how responsible prompt engineering serves as a crucial bridge between AI development and deployment, enabling organizations to fine-tune AI outputs without modifying underlying model architectures. This approach aligns with broader "Responsibility by Design" principles, embedding ethical considerations directly into the implementation process rather than treating them as post-hoc additions. The article concludes by identifying key research directions and practical guidelines for advancing the field of responsible prompt engineering.