This paper aims at developing a convolutional neural network (CNN)-based tool that can automatically detect the left-turning vehicles (right-hand traffic rule) at signalized intersections and extract their trajectories from a recorded video. The proposed tool uses a region-based CNN trained over a limited number of video frames to detect moving vehicles. Kalman filters are then used to track the detected vehicles and extract their trajectories. The proposed tool achieved an acceptable accuracy level when verified against the manually extracted trajectories, with an average error of 16.5 cm. Furthermore, the trajectories extracted using the proposed vehicle tracking method were used to demonstrate the applicability of the minimum-jerk principle to reproduce variations in the vehicles’ paths. The effort presented in this paper can be regarded as a way forward toward maximizing the potential use of deep learning in traffic safety applications.