A euphemism for sexual intercourse. More specifically, the act of performing a Russian Unicorn. Where one straps a dildo to his/her head, and then has sex. It comes from the BadLipReading video ""Russian Unicorn" — a bad lip reading of Michael Bublé."
Chris: "Dude i heard your girl is going to spend the night"
Edward: "Yeah! We are totally going to Shoot a Russian Unicorn!"