If you want to carry a wire tire, then you can fold it by shaping it to an oval, bring the ends up into a saddle shape so the ends come up to meet each other, and overlap. The middles are overlapped under, and it all settles into three loops without any kincks, then you can strap it down. Look online for instructions on how to fold a bandsaw blade. Try it with a belt first, remember, no twists.
Another option is to form it into a saddle shape and use it as the tiedown for the the rear rack, You will need little ties to tension it up, but being rubber, it makes a good tie down, because it's sticky enough to hold stuff together.