Unmanned aerial vehicle (UAVs) are a key platform in the sixth generation (6G) communication networks, where integrated sensing and communication (ISAC) is also a promising technology that requires real-time channel estimation. This paper proposes a robust and efficient angle-of-arrival (AOA) estimation method based on a field-trained neural network (NN) for low-latency UAV ISAC applications. In this method, the NN is pre-trained quickly in the field with each receiving antenna element's channel state information (CSI) and the transceivers' locations. We extract the channel multi-paths from the CSI and calculate the path phases as the training data set in real time. Then the pre-trained NN is used for high-efficient AoA estimation in real time. A real-time UAV channel sounder is utilized to verify the proposed method. The measurement results show that the proposed field-trained estimation method is faster and more robust compared with the traditional method and fixed-trained NN. The proposed angle estimation method is valuable for UAV channel estimation and low-latency UAV ISAC applications.