Butcher/Cooking Twine - safe for BBQ?
I've used butchers twine on the grill many times with only the cut ends charring a bit.  As the meat cooks the twine absorbs some of the fluid that it exudes, which evaporates and cools the twine some.  By the time the twine chars the meat has started to shrink and usually the shape has at least started to set.

As an alternative you can use wire. Stainless steel wire for this purpose can be purchased online from many grilling and BBQ retailers. For larger projects, like whole hog rotisserie, I've seen people use chicken wire fencing material.  Just make sure to thoroughly clean off any oil or coating that may be on the wire before using it on food.