Wireless Physical Layer Identification (WPLI) system aims at identifying or classifying authorized devices based on the unique Radio Frequency Fingerprints (RFFs) extracted from their radio frequency signals at the physical layer. Current works of WPLI focus on demonstrating system feasibility based on experimental error performance of WPLI with a fixed number of users. While an important question remains to be answered: what's the user number that WPLI can accommodate using different RFFs and receiving equipment. The user capacity of the WPLI can be a major concern for practical system designers and can also be a key metric to evaluate the classification performance of WPLI. In this work, we establish a theoretical understanding on user capacity of WPLI in an information-theoretic perspective. We apply information-theoretic modeling on RFF features of WPLI. An information-theoretic approach is consequently proposed based on mutual information between RFF and user identity to characterize the user capacity of WPLI. Based on this theoretical tool, the achievable user capacity of WPLI is characterized under practical constrains of off-the-shelf receiving devices. Field experiments on classification error performance are conducted for the validation of the information-theoretic user capacity characterization.