I do believe that there is kite string that is all cotton and essentially the same thing as kitchen twine, at least that used to be the case when I was growing up in the 50s and 60s. You might be able to tell from the label, which should say that it's 100% cotton. I sure wouldn't go for that powdered glass stuff that Panfusine mentions!! And you'll want to watch out for synthetics that could melt or vaporize some chemical contaminants.

I don't think that's a very good idea. But I've often subbed linen fishing twine.

YOIKES!! Doesn't kite string come coated with powdered glass? (the glass comes in handy to 'cut' opponents kites in competitions..)

Hmmm . . doesn't seem like a good idea to me. Kite string could have polymer components or coatings that you probably don't want in contact with food that's being cooked.

Butcher's twine, which appears to be made from cotton, would seem to be a better way to go.

There may even be an organic butcher's twine movement afoot somewhere.