Is it permissible to play rope as a sport?

There is no harm in exercising with a rope or other means that cause no harm, even for a Muslim woman. This is based on what was narrated by Aisha, may Allah be pleased with her, who said: "The Prophet raced with me and I outran him. When I gained some weight, he raced with me and outran me, and he said: 'This is for that.'"