Bridges are often at risk due to the effects of natural disasters, such as earthquakes and typhoons. Bridge inspection assessments normally focus on cracks. However, numerous concrete structures with cracked surfaces are highly elevated or over water, and is not easily accessible to a bridge inspector. Furthermore, poor lighting under bridges and a complex visual background can hinder inspectors in their identification and measurement of cracks. In this study, cracks on bridge surfaces were photographed using a UAV-mounted camera. A YOLOv4 deep learning model was used to train a model for identifying cracks; the model was then employed in object detection. To perform the quantitative crack test, the images with identified cracks were first converted to grayscale images and then to binary images the using local thresholding method. Next, the two edge detection methods, Canny and morphological edge detectors were applied to the binary images to extract the edges of the cracks and obtain two types of crack edge images. Then, two scale methods, the planar marker method, and the total station measurement method, were used to calculate the actual size of the crack edge image. The results indicated that the model had an accuracy of 92%, with width measurements as precise as 0.22 mm. The proposed approach can thus enable bridge inspections and obtain objective and quantitative data.