Unmanned aerial vehicle (UAV) are a key platform in the sixth generation (6G) communication networks, which has the ability to significantly enhance the connectivity and communication efficiency. This paper proposes a robust and efficient angle-of-arrival (AoA) estimation method based on a field-trained neural network (NN) for air-to-ground (A2G) channel measurement applications. In this method, a real-time UAV channel sounder is utilized to obtain the complex channel impulse response (CIR). Firstly, we identify the line-of-sight (LoS) path from the complex CIR via a random forest (RF) classifier and calculate the LoS path phase as the input data set in the real-time stage. Then the NN is pre-trained quickly in the field by each receiving antenna element's LoS path phase and the corresponding AoAs according to the locations of transceivers. Finally, the pre-trained NN is used for high-efficient LoS and non-LoS (NLoS) AoA estimation in real-time. To validate the proposed method, a channel measurement campaign is carried out in a campus scenario at 3.6 GHz. The estimated results are in good agreements with the measurement data and theoretical for the LoS and NLoS cases. In addition, the proposed field-trained estimation method is more computationally efficient and more robust compared with the traditional methods. The proposed angle estimation method is also valuable for future A2G channel measurement, enabling more reliable and efficient connectivity in dynamic and complex environments. Index Terms-Unmanned aerial vehicle (UAV), angle-of-arrival (AoA) estimation, field-trained neural network (NN), air-toground (A2G) channel, channel measurement.