Smart glasses have become more prevalent as they provide an increasing number of applications for users. They store various types of private information or can access it via connections established with other devices. Therefore, there is a growing need for user identification on smart glasses. In this paper, we introduce a low-power and minimally-obtrusive system called SonicID, designed to authenticate users on glasses. SonicID extracts unique biometric information from users by scanning their faces with ultrasonic waves and utilizes this information to distinguish between different users, powered by a customized binary classifier with the ResNet-18 architecture. SonicID can authenticate users by scanning their face for 0.06 seconds. A user study involving 40 participants confirms that SonicID achieves a true positive rate of 97.4%, a false positive rate of 4.3%, and a balanced accuracy of 96.6% using just 1 minute of training data collected for each new user. This performance is relatively consistent across different remounting sessions and days. Given this promising performance, we further discuss the potential applications of SonicID and methods to improve its performance in the future.