We already have the RSS feed, I can't imagine it's very hard to convert that into a Facebook app thingy. Should be called 'Wikimedia Commons Picture of the Day' or just 'Wikimedia Commons'.
http://tools.wikimedia.de/~daniel/potd/potd.php
http://developers.facebook.com/
Facebook currently has 94 'photos' apps http://www.facebook.com/apps/index.php?category=11 . I only noticed one 'general POTD' style one: http://www.facebook.com/apps/application.php?id=2447176338&b .
Anyone feel like a challenge? :)
cheers Brianna