Structural health monitoring (SHM) is essential for the early detection of infrastructure defects, such as cracks in concrete bridge pier. but often faces challenges in efficiency and accuracy in complex environments. Although the Segment Anything Model (SAM) achieves excellent segmentation performance, its computational demands limit its suitability for real-time applications on edge devices. To address these challenges, this paper proposes Crack-EdgeSAM, a self-prompting crack segmentation system that integrates YOLOv8 for generating prompt boxes and a fine-tuned EdgeSAM model for crack segmentation. To ensure computational efficiency, the method employs ConvLoRA, a Parameter-Efficient Fine-Tuning (PEFT) technique, along with DiceFocalLoss to fine-tune the EdgeSAM model. Our experimental results on public datasets and the climbing robot automatic inspections demonstrate that the system achieves high segmentation accuracy and significantly enhanced inference speed compared to the most recent methods. Notably, the system processes 1024 x 1024 pixels images at 46 FPS on our PC and 8 FPS on Jetson Orin Nano.