Real2Sim is becoming increasingly important with the rapid development of surgical artificial intelligence (AI) and autonomy. In this work, we propose a novel Real2Sim methodology, Instrument-Splatting, that leverages 3D Gaussian Splatting to provide fully controllable 3D reconstruction of surgical instruments from monocular surgical videos. To maintain both high visual fidelity and manipulability, we introduce a geometry pre-training to bind Gaussian point clouds on part mesh with accurate geometric priors and define a forward kinematics to control the Gaussians as flexible as real instruments. Afterward, to handle unposed videos, we design a novel instrument pose tracking method leveraging semantics-embedded Gaussians to robustly refine per-frame instrument poses and joint states in a render-and-compare manner, which allows our instrument Gaussian to accurately learn textures and reach photorealistic rendering. We validated our method on 2 publicly released surgical videos and 4 videos collected on ex vivo tissues and green screens. Quantitative and qualitative evaluations demonstrate the effectiveness and superiority of the proposed method. Our code is available at https://github.com/jinlab-imvr/Instrument-Splatting .