Yes it does but it is getting updated right now and will be available in a few weeks to download from app store. Untill then you can download and use the app tapatalk to browse avsforum on your mobile.
I don't think it is an app actually but rather a mobile site written in HTML5 and functional across all mobile device platforms. I've been using the regular site on my phone for a while and although it works well it is sometimes tough to navigate.
Tapatalk! Although all the functions don't work on a forum like this. I can't post in a thread if its a sticky. And PM's don't work. Same thing with Overclock.net as they recently went to this type of forum.
But its good enough just to browse some threads.
As far as the mobile site. I don't mess with apple but in android you can put a bookmark link to avs on your home screen. Which really makes it no different than an app since the layout is very similar.