Are you seeing the tutorial message on how to swing with the rope using Circle? You should be on the rope already by that point. I think you grab onto the rope automatically. Did you destroy the barriers before going for the rope?
Also, note that the jumping in GoW is not all that great. Experiment with how long you press Circle before pressing Circle again. You can't double jump past a certain point, so you kind of have to press Circle then Circle again almost immediately, but don't let go, because the second Circle press keeps you jumping as long as you keep it pressed. Meanwhile, you should be aligned with the rope and grab it.