Cell-level quantitative features of retinal ganglion cells (GCs) are potentially important biomarkers for improved diagnosis and treatment monitoring of neurodegenerative diseases such as glaucoma, Parkinson's disease, and Alzheimer's disease. Yet, due to limited resolution, individual GCs cannot be visualized by commonly used ophthalmic imaging systems, including optical coherence tomography (OCT), and assessment is limited to gross layer thickness analysis. Adaptive optics OCT (AO-OCT) enables in vivo imaging of individual retinal GCs. We present an automated segmentation of GC layer (GCL) somas from AO-OCT volumes based on weakly supervised deep learning (named WeakGCSeg), which effectively utilizes weak annotations in the training process. Experimental results show that WeakGCSeg is on par with or superior to human experts and is superior to other state-of-the-art networks. The automated quantitative features of individual GCLs show an increase in structure-function correlation in glaucoma subjects compared to using thickness measures from OCT images. Our results suggest that by automatic quantification of GC morphology, WeakGCSeg can potentially alleviate a major bottleneck in using AO-OCT for vision research.