I've resorted to the FB Mobile site which isn't a bad compromise really, but I was going a little crazy trying to find the option within the FB App, just wondering if it exists?
Yes, there is a way to do so in the mobile app.
I am using Facebook App Version 1.8.1 on a Motorola Droid 3.
The process I did to set a picture as my profile picture was as follows:
It may be slightly different on your device; however it is possible to do this in the latest Facebook version on the desired photo.
For honeycomb you could go into pics on your phone and hit set as and Facebook profile was an option. Now that my phone has ICS, it only gives me the option of setting as wallpaper or contact photo. With ICS you can only set profile pic from pics already on Facebook, but not upload from pics on phone. It's very annoying.