We study object motion path editing in videos, where the goal is to alter a target object's trajectory while preserving the original scene content. Unlike prior video editing methods that primarily manipulate appearance or rely on point-track-based trajectory control, which is often challenging for users to provide during inference, especially in videos with camera motion, we offer a practical, easy-to-use approach to controllable object-centric motion editing. We present Trace, a framework that enables users to design the desired trajectory in a single anchor frame and then synthesizes a temporally consistent edited video. Our approach addresses this task with a two-stage pipeline: a cross-view motion transformation module that maps first-frame path design to frame-aligned box trajectories under camera motion, and a motion-conditioned video re-synthesis module that follows these trajectories to regenerate the object while preserving the remaining content of the input video. Experiments on diverse real-world videos show that our method produces more coherent, realistic, and controllable motion edits than recent image-to-video and video-to-video methods.