In recent years, RF fingerprinting (RFF) has emerged as a promising technology for wireless device authentication. However, temporal variations in device load and temperature, along with channel effects, lead to inconsistencies in RFF distributions between training and testing phases. As a result, deep learning (DL)-based recognition models often suffer from degraded performance. To address this problem, we propose the first test-time-adaptation (TTA) approach to improve the domain generalization ability of RFF recognition models. We first analyze the causes of time-varying RFF distribution shifts, such as carrier frequency offset (CFO), and develop a physical impairment-based data augmentation strategy. Based on this, we further propose a physically information-aware prototype to guide the model for TTA. Our method requires no model retraining or labeled test samples, and is a lightweight, nonparametric solution. Finally, our approach is extensively evaluated using mobile phones with the IEEE 802.11 orthogonal frequency division multiplexing (OFDM) system, which demonstrates that our scheme can effectively improve RFF average recognition performance by about 7.8%.