In the field of human-computer interaction (HCI), handwriting trajectory tracking and recognition have attracted significant attention due to their wide range of applications. However, many existing approaches rely on handheld devices and are highly susceptible to factors such as environmental conditions, location, and writing style. To overcome these limitations, we propose AirWrite, a novel contactless aerial system for handwriting trajectory tracking and recognition using mmWave technology. We introduce a signal clipping method based on the Doppler effect caused by user actions to accurately remove non-handwriting signals in the time domain. Additionally, we analyze power variations within the signal frequency interval to determine the handwriting frequency and employ a band-pass filter to eliminate dynamic environmental noise effectively. Through extensive experiments, we demonstrate that AirWrite can precisely track handwriting trajectories in noisy environments regardless of distance, angle, handwriting speed, character size, or in the presence of obstacles. Furthermore, we present an effective handwritten character recognition method for AirWrite that recognizes alphabets, numbers, and words. AirWrite can achieve an average accuracy of over 96% with only a 34 KB small dataset within 0.15 s for recognition.