Heres how it was when I was 13: I never had my own cell phone, however I would borrow my mom or dad's when I would go out with friends. I got my own cell phone when I was a freshman in high school, and it was a hand me down of my mom's old one and I wasnt allowed to take it anywhere but when I went out. It wasnt until late, late, late sophomore year, maybe the summer before Junior year, that I got my own.
Short answer: dont buy him one until you feel he actually needs it, it is obvious he just wants one to show off right now.