Determination of the pose of workpieces is important for robotic applications in manufacturing, including handling, assembly, machining and welding. Established methods based on 3D sensors may fail for workpieces with highly reflective materials. In this paper, we take advantage of recent development in machine learning to determine the pose of reflective workpieces without the use of depth data. Our proposed method is based on deep iterative matching of image data of the workpiece with a computer-aided design model. Starting with an initial estimate of the workpiece pose, the method iteratively aligns the computer-aided design model projections with an image of the actual workpiece, adjusting the pose until computer-aided design model matches the image of the workpiece. The deep learning-based approach optimizes this alignment by updating the pose estimate at each iteration, achieving high precision even for geometrically complex or reflective surfaces. This refinement process enhances accuracy in robotic applications where precise workpiece positioning is critical, such as in automated welding and assembly tasks. We use photorealistic rendering to create two datasets for pretraining the network, which reduces both training time and the need for real labeled data. After the network is trained on synthetic data, it is fine-tuned and tested on real images of reflective aluminium workpieces. We show that the proposed deep iterative matching method outperforms established methods based on iterative closest point with two 3D scanners due to large errors in the scans caused by reflections.