No. They are completely different cartridges.
The AK-47 is a Soviet/Russian "assault rifle" originally designed for the 7.62x39mm (Soviet M43) cartridge. The actual diameter of the bullet is .310-.312". The M43 has similar ballistics to a US 30-30 Win.
On the other hand, 308 Winchester is the civilian version of the US Military 7.62x51mm NATO, which uses a .308" diameter bullet. Both versions use a heavier bullet, faster velocity and higher pressure.
Subsequent versions of the AK-47 have been designed for many other cartridges, including .410, 20 & 12 gauge shotgun rounds. However, because of higher pressure and the longer length of the 308 round (51mm vs. 39mm), it would be extremely difficult and impractical to attempt to re-chamber a AK-47 rifle to 308 Win.
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