Kinda of odd actually, since AK-47s are not required to be turned in. Anything larger than 7.62mm must be turned in, but that caliber or smaller, including full automatics, can be possesed in their home or business. Better than here actually. Here is the CENTCOM release on the matter. But the gist of it is:
Unauthorized weapons are defined as: automatic firearms firing ammunition larger than 7.62mm; machine guns or crew-served weapons; anti-tank weapons; anti-aircraft weapons; indirect fire weapons; all armored vehicles or self-propelled weapons; and high explosives and explosive devices.
No one in Iraq, unless authorized, may possess, conceal, hide or bury these weapons. No one can trade, sell, barter, give or exchange automatic or heavy weapons with or to any person who is not an authorized representative of Coalition forces.
...
Small arms--including automatic rifles firing ammunition up to 7.62mm, semi-automatic rifles, shotguns, and pistols--may be possessed in homes and in a place of business. Small arms must remain at these sites and may not be taken out in public.
Only authorized persons may possess small arms in public places and those authorized persons will be issued a temporary weapons card (TWC) by Coalition Commanders.