Thanks to his high knowledge in Repair, the Vault Dweller has modified a Red Ryder BB gun so it absorbs and propels the surrounding air, forming a ball of air, instead of using ammunition. But since air is hard to control, its damage varies randomly from very low to very powerful.
The Red Ryder BB gun was also a powerful weapon obtainable in Wasteland, the predecessor game to the Fallout series. In Highpool, the party has to fight the child whose dog (Rex) "was gunned down by vigilante Rangers," or it could be acquired via cheat.
The Red Ryder himself is another reference to the BB gun and Wasteland, he shows up to fight the Rangers in revenge should they murder the children making fun of them after falling into the river.