Guidewire segmentation during endovascular interventions holds the potential to significantly enhance procedural accuracy, improving visualization and providing critical feedback that can support both physicians and robotic systems in navigating complex vascular pathways. Unlike supervised segmentation networks, which need many expensive expert-annotated labels, sim-to-real domain adaptation approaches utilize synthetic data from simulations, offering a cost-effective solution. The success of models like Segment-Anything (SAM) has driven advancements in image segmentation foundation models with strong zero/few-shot generalization through prompt engineering. However, they struggle with medical images like X-ray fluoroscopy and the domain-shifts of the data. Given the challenges of acquiring annotation and the accessibility of labeled simulation data, we propose a sim-to-real domain adaption framework with a coarse-to-fine strategy to adapt SAM to X-ray fluoroscopy guidewire segmentation without any annotation on the target domain. We first generate the pseudo-labels by utilizing a simple source image style transfer technique that preserves the guidewire structure. Then, we develop a weakly supervised self-training architecture to fine-tune an end-to-end student SAM with the coarse labels by imposing consistency regularization and supervision from the teacher SAM network. We validate the effectiveness of the proposed method on a publicly available Cardiac dataset and an in-house Neurovascular dataset, where our method surpasses both pre-trained SAM and many state-of-the-art domain adaptation techniques by a large margin. Our code will be made public on GitHub soon.