As an emerging innovation paradigm that balances the demand for profit growth and social value, responsible innovation has been increasingly recognized by enterprises as an effective approach for them to proactively assume social responsibilities and achieve sustainable development goals. In view of the widespread appeal to promote the sustainable development of agriculture with scientific and technological innovation, it is extremely necessary to discuss the topic of responsible innovation in agriculture. Based on the resource orchestration theory, this study constructed a theoretical model that explores how green entrepreneurial orientation influences enterprise responsible innovation. The research data from 248 agricultural enterprises were analyzed using the hierarchical regression and MEDCURVE macro-program. The empirical results indicated that: (1) green entrepreneurial orientation positively influences green supply chain integration; (2) green supply chain integration, in turn, has an inverted U-shaped influence on enterprise responsible innovation; (3) green supply chain integration acts as a mediator between green entrepreneurial orientation and enterprise responsible innovation; and (4) big data analytics capability positively moderates the linear relationship between green entrepreneurial orientation and green supply chain integration, as well as the inverted U-shaped relationship between green supply chain integration and enterprise responsible innovation. This study has not only enriched the research on the formation mechanism of enterprise responsible innovation, but also provided practical enlightenment for managers and policy makers to promote enterprise responsible innovation.