Camera-to-robot calibration is crucial for visionbased robot control and requires effort to make it accurate. Recent advancements in markerless pose estimation methods have eliminated the need for time-consuming physical setups for camera-to-robot calibration. While the existing markerless pose estimation methods have demonstrated impressive accuracy without the need for cumbersome setups, they rely on the assumption that all the robot joints are visible within the camera's field of view. However, in practice, robots usually move in and out of view, and some portion of the robot may stay out-of-frame during the whole manipulation task due to real-world constraints, leading to a lack of sufficient visual features and subsequent failure of these approaches. To address this challenge and enhance the applicability to visionbased robot control, we propose a novel framework capable of estimating the robot pose with partially visible robot manipulators. Our approach leverages the Vision-Language Models for fine-grained robot components detection, and integrates it into a keypoint-based pose estimation network, which enables more robust performance in varied operational conditions. The framework is evaluated on both public robot datasets and self-collected partial-view datasets to demonstrate our robustness and generalizability. As a result, this method is effective for robot pose estimation in a wider range of realworld manipulation scenarios.