Gestational age estimation at time of birth is critical for determining the degree of prematurity of the infant and for administering appropriate postnatal treatment. We present a fully automated algorithm for estimating gestational age of premature infants through smartphone lens imaging of the anterior lens capsule vasculature (ALCV). Our algorithm uses a fully convolutional network and blind image quality analyzers to segment usable anterior capsule regions. Then, it extracts ALCV features using a residual neural network architecture and trains on these features using a support vector machine-based classifier. The classification algorithm is validated using leave-one-out cross-validation on videos captured from 124 neonates. The algorithm is expected to be an influential tool for remote and point-of-care gestational age estimation of premature neonates in low-income countries. To this end, we have made the software open source.