Causal representation learning (CRL) has emerged as a powerful unsupervised framework that (i) disentangles the latent generative factors underlying high-dimensional data, and (ii) learns the cause-and-effect interactions among the disentangled variables. Despite extensive recent advances in identifiability and some practical progress, a substantial gap remains between theory and real-world practice. This paper takes a step toward closing that gap by bringing CRL to robotics, a domain that has motivated CRL. Specifically, this paper addresses the well-defined robot pose estimation -- the recovery of position and orientation from raw images -- by introducing Robotic Pose Estimation via Score-Based CRL (ROPES). Being an unsupervised framework, ROPES embodies the essence of interventional CRL by identifying those generative factors that are actuated: images are generated by intrinsic and extrinsic latent factors (e.g., joint angles, arm/limb geometry, lighting, background, and camera configuration) and the objective is to disentangle and recover the controllable latent variables, i.e., those that can be directly manipulated (intervened upon) through actuation. Interventional CRL theory shows that variables that undergo variations via interventions can be identified. In robotics, such interventions arise naturally by commanding actuators of various joints and recording images under varied controls. Empirical evaluations in semi-synthetic manipulator experiments demonstrate that ROPES successfully disentangles latent generative factors with high fidelity with respect to the ground truth. Crucially, this is achieved by leveraging only distributional changes, without using any labeled data. The paper also includes a comparison with a baseline based on a recently proposed semi-supervised framework. This paper concludes by positioning robot pose estimation as a near-practical testbed for CRL.