The sustainable retrofitting of ageing reinforced concrete (RC) infrastructure requires decision-making frameworks that can simultaneously account for structural performance, environmental impact, and economic feasibility. Digital Twins (DTs) offer a promising paradigm for linking physical assets with virtual representations; however, most existing DT implementations in structural engineering remain descriptive, static, and dependent on manual expert judgement. In particular, the lack of adaptive intelligence and autonomous reasoning limits their usefulness for retrofit decision-making. This study proposes an adaptive, agentic Digital Twin framework for retrofit decision-making in reinforced concrete structures, demonstrated at the laboratory scale using RC beam specimens. The proposed DT integrates three tightly coupled components: (i) physics-based structural models calibrated using experimental measurements and sensor data; (ii) machine-learning models trained to predict the environmental impact (e.g. embodied carbon associated with retrofit materials) and economic performance (e.g. life-cycle cost and retrofit efficiency) of alternative intervention strategies; and (iii) an agentic AI layer that autonomously evaluates retrofit scenarios and recommends optimal actions under multi-objective constraints. The agentic component continuously updates its recommendations as new data become available, enabling adaptive learning within the framework. The methodology is validated through laboratory tests on scaled RC beams subjected to damage and retrofit scenarios. Experimental observations are assimilated into the DT to update structural states, while surrogate learning models estimate the environmental and economic indicators associated with each retrofit option. Results demonstrate that the agentic DT consistently identifies retrofit strategies that satisfy structural performance requirements while reducing environmental footprint and life-cycle cost compared with static decision approaches. The proposed framework advances Digital Twin research by illustrating how agentic AI can transform DTs from passive monitoring tools into adaptive decision-support systems for structural sustainability. Although demonstrated at the laboratory scale, the framework provides a scalable foundation for future application to full-scale concrete infrastructure retrofitting.