Objectives: To develop and validate an open-source deep learning model for automatically quantifying scapular and glenoid morphology using CT images of normal subjects and patients with glenohumeral osteoarthritis. Materials and Methods: First, we used deep learning to segment the scapula from CT images and then to identify the location of 13 landmarks on the scapula, 9 of them to establish a coordinate system unaffected by osteoarthritis-related changes, and the remaining 4 landmarks on the glenoid cavity to determine the glenoid size and orientation in this scapular coordinate system. The glenoid version, glenoid inclination, critical shoulder angle, glenopolar angle, glenoid height, and glenoid width were subsequently measured in this coordinate system. A 5-fold cross-validation was performed to evaluate the performance of this approach on 60 normal/non-osteoarthritic and 56 pathological/osteoarthritic scapulae. Results: The Dice similarity coefficient between manual and automatic scapular segmentations exceeded 0.97 in both normal and pathological cases. The average error in automatic scapular and glenoid landmark positioning ranged between 1 and 2.5 mm and was comparable between the automatic method and human raters. The automatic method provided acceptable estimates of glenoid version (R2 = 0.95), glenoid inclination (R2 = 0.93), critical shoulder angle (R2 = 0.95), glenopolar angle (R2 = 0.90), glenoid height (R2 = 0.88) and width (R2 = 0.94). However, a significant difference was found for glenoid inclination between manual and automatic measurements (p < 0.001). Conclusions: This open-source deep learning model enables the automatic quantification of scapular and glenoid morphology from CT scans of patients with glenohumeral osteoarthritis, with sufficient accuracy for clinical use.