In my experience it was about 6 MOA, using a Chinese MAK90, (which, except for the stock, are considered to be decent AK's). A particularly good one like a Valmet would probably perform somewhat better. The problem seems to be mostly related to the cartridge. I have read that even AR's chambered in 7.62x39 tend to have disappointing accuracy.
If you go over to AR15.com and click on the AK47 tab you can find many threads on this subject. The consensus seems to be that AK's in 7.62x39 are capable of somewhere between 4 and 8 MOA depending on the gun in question and who you ask. AK's in other calibers do much better, but they don't seem to have the potential to be made truly accurate.
That’s because most of the 7.62X39 shot in them is cheap Russian Wolf and old surplus ammo. Accurate it ain’t The 7.62X39 ain’t no slouch itself. Various bolt-gun makers chamber it with good results. Heck the 6mmPPC widely regarded as one of the most naturally accurate cartridges ever made is a kissing cousin in design to the “Russian Short”. Also Ak’s aren’t accurate because of their designed loose tolerances. The good side of this is it allows for their legendary reliability.