Sure! Go to a site like quadratec.com and search for "mirror brackets" - you'll get some weird results for light brackets, but there are also several mirror mounting brackets to pick from.
Lots of us run Jeeps with no doors, so we need to move the mirrors. And on my CJ, that's where they put them in the first place (doors were an extra option back then).
Windshield mounted mirrors do NOT work as well - it's hard to get the angles right, and it seems like the doors always find a way to smack them. But it does work.
But we sell replacement JK mirrors now, so you can always get a replacement if they break. (hey, I get paid to do some marketing!).