Multiple object tracking (MOT), a popular subject in computer vision with broad application areas, aims to detect and track multiple objects across an input video. However, recent learning-based MOT methods require strong supervision on both the bounding box and the ID of each object for every frame used during training, which induces a heightened cost for obtaining labeled data. In this paper, we propose a weakly-supervised MOT framework that enables the accurate tracking of multiple objects while being trained without object ID ground truth labels. Our model is trained only with the bounding box information with a novel masked warping loss that drives the network to indirectly learn how to track objects through a video. Specifically, valid object center points in the current frame are warped with the predicted offset vector and enforced to be equal to the valid object center points in the previous frame. With this approach, we obtain an MOT accuracy on par with those of the state-of-the-art fully supervised MOT models, which use both the bounding boxes and object ID as ground truth labels, on the MOT17 dataset.