The adoption of cyber-physical systems and jobsite intelligence that connects design models, real-time site sensing, and autonomous field operations can dramatically enhance digital management in the construction industry. This paper introduces BIM2RDT (Building Information Models to Robot-Ready Site Digital Twins), an agentic artificial intelligence (AI) framework designed to transform static Building Information Modeling (BIM) into dynamic, robot-ready digital twins (DTs) that prioritize safety during execution. The framework bridges the gap between pre-existing BIM data and real-time site conditions by integrating three key data streams: geometric and semantic information from BIM models, activity data from IoT sensor networks, and visual-spatial data collected by robots during site traversal. The methodology introduces Semantic-Gravity ICP (SG-ICP), a point cloud registration algorithm that leverages large language model (LLM) reasoning. Unlike traditional methods, SG-ICP utilizes an LLM to infer object-specific, plausible orientation priors based on BIM semantics, improving alignment accuracy by avoiding convergence on local minima. This creates a feedback loop where robot-collected data updates the DT, which in turn optimizes paths for missions. The framework employs YOLOE object detection and Shi-Tomasi corner detection to identify and track construction elements while using BIM geometry as a priori maps. The framework also integrates real-time Hand-Arm Vibration (HAV) monitoring, mapping sensor-detected safety events to the digital twin using IFC standards for intervention. Experiments demonstrate SG-ICP's superiority over standard ICP, achieving RMSE reductions of 64.3%--88.3% in alignment across scenarios with occluded features, ensuring plausible orientations. HAV integration triggers warnings upon exceeding exposure limits, enhancing compliance with ISO 5349-1.