When you say a rope braided rug, do you mean a plaited rope rug (SEWN TOGETHER IN ONE CONTINUOUS COIL) ? If that's it, then use a Sail needle and twine.. ..You will also need something to help you push the needle through the rug, such as a padded block.
Here is a fancy one https://www.hometalk.com/42351264/diy-rope-rug
Or a more plain one https://www.hometalk.com/41113630/diy-round-rope-area-rug
So a traditional braided rug has the braids sewn together to create a rug... I guess it'd be the same only with rope instead of fabric or yarn. Create your braid with the rope, then stitch it together, starting in the center by coiling it and stitching together where the edges of the coils meet. It might be a little difficult to stitch some rope together, but I'm sure there's a way. An rounded upholstery needle will help tremendously!