I googled this post title in many different configurations, hoping to get an answer. Many of the choices were for ads wanting you to visit “XYZ Oriental Rugs” to purchase a rug or have their staff re-weave your carpet. Some of the searches revealed how to re-sew a broken braided rag rug. But two of the best solutions were from “rug chick” and “Mr. Fix-it.” They recommended glueing the rug back together or duct-taping it on the reverse side.
I gathered some home-spun wool yarns, as well as a couple of thicker cotton yarns. You may see a match in the photo, but each was a shade off. This won’t be easy to repair, since the warp threads–which appear to be cotton–are thin and broken (see below).
Since I didn’t find an answer to my question on the internet, I plan to find a large needle and some strong cotton thread and give it a go on my own. If it works and looks decent, maybe I will make my own You-tube video on how to re-weave a handwoven rug.