The intelligent transportation system (ITS) is committed to ensuring safe and effective next-generation traffic throughout a city. However, such efficient operation on urban traffic networks needs the support of big traffic data, especially Turning Movement Counts (TMC) at intersections. Generally, TMC data are more challenging to collect due to labor cost and accuracy problems. In this paper, we leverage the capabilities of Unmanned Aerial Vehicles (UAV) to collect real-time TMC data in a cost-efficient way. We proposed a real-time TMC data collection framework based on a live video stream. The vehicle tracking capability is boosted by multiple object tracking based on tracking by detection. In addition, a challenging case study was conducted, and our results demonstrate the feasibility and robustness of the proposed TMC data collection framework. Specifically, with a GTX 1650 graphics card, about 10 FPS can be achieved in real-time for the TMC data collection. The overall accuracy is 91.93%, and the best case is over 98% accurate. In the context of miscounting, the major reason is due to ID switching caused by background occlusion. The proposed framework is expected to provide real-time data for traffic capacity analysis and advanced traffic simulation such as digital twins.