Pop the popcorn in an air popper, and put in a large bowl.
In a medium saucepan, melt butter, honey, and arrowroot powder together over medium heat. Stir constantly.
Let mixture come to a boil and let it cook (while stirring) for about 5 minutes to thicken. Remove from heat.
Pour half of the honey mixture over the bowl of popcorn. Using two forks, toss to coat the popcorn with the honey. Then pour the rest of the honey mixture over the rest of the popcorn, attempting to cover every piece.
Allow the popcorn to cool a bit, then form into balls with buttered hands.
Lay the balls on waxed paper and allow to harden. (If it's not hardening fast enough, the balls can be put into the refrigerator for about 10 minutes.)