Next-generation wireless networks are increasingly large-scale, heterogeneous, and dynamic, posing significant challenges to network modeling and control. Digital twins offer a promising solution, but existing approaches typically rely on static models and decouple twin construction from network orchestration, limiting adaptability. Meanwhile, large language models (LLMs) provide strong reasoning capabilities but struggle with graph-structured data and are highly sensitive to prompt design, making inference unreliable. In this paper, we propose Janus, an agentic LLM-based framework that unifies digital twin construction and network orchestration within a closed-loop system. At the core of Janus is a novel NetTwin agent, which introduces a new one-agent, two-role paradigm, enabling a single agent to simultaneously construct the digital twin from partial observations while performing task-driven network decision-making. To realize this, we design a modular architecture with three functional roles, including planner, modeler, and coder, along with a newly designed unified prompt module that further enhances graph reasoning robustness. Extensive evaluations on wireless networks with up to 200 nodes and two representative tasks, including user association and SAGIN routing, show that Janus achieves over 90% digital twin accuracy and near-optimal performance with gaps within 10.53%, while maintaining moderate computational overhead. These results demonstrate the effectiveness, scalability, and generalizability of Janus, paving the way for AI-native autonomous wireless network orchestration.

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