Possibly. You can't import a rifle in a "non-sporting" configuration. Also, you cannot assemble a rifle out of imported parts that would not be importable. And, since the expiration of the AW ban, you can build pretty much what you want from American parts.
The grey area is when you combine a mix of American and imported parts. Our friends at the ATF came up with a list of 20 major parts. Not all guns even have all 20 parts (some guns don't have an op rod, for example.) Your assembled rifle can have no more than 10 imported parts of the 20 major parts.
It's odd, that a rifle assembled on a US made receiver, by an American, in the United States, could possibly be a violation of the "sporting purposes" nonsense expressed in the gun control act of 1968, as amended by executive fiat in 1989. However, the US receiver will not count against the 10 imported part limit, enabling you to add another imported part.
Here the list of parts:
1. Frames, Receivers
2. Barrels
3. Barrel extensions
4. Mounting blocks
5. Muzzle attachments
6. Bolts
7. Bolt carriers
8. Operating rods
9. Gas piston
10. Trigger housing
11. Trigger
12. Hammer
13. Sear
14. Dis-connectors
15. Butt stocks
16. Pistol grips
17. Forearms, hand guards
18. Magazine bodies
19. Followers
20. Floor plates
Now that it's become a national pastime to assemble semiautomatic rifles out of imported parts "kits" and a new receiver, a market for US made replacement parts has sprung up. You need to use enough US parts to comply with the "10 or less imported parts" law. An easy way to comply with the law is to use US made magazines (eliminates 3 imported parts.) That's a little iffy, because if you happen to have foreign mags laying about, that magazine when inserted into that weapon might push you over the 10 imported part limit. A "safer" way to comply would be to replace your trigger group (hammer, trigger and sear.) Then you could use any magazine.. no danger of being charged with "constructive possession".
This is old hat to guys who assemble FAL or AK "kits" onto new receivers. It's more likely to be a surprise to SKS shooters. Those rifles are importable as-is, then you add a few "features" that make it non-importable, and thus subject to the 922(r) rules. For example, add a US made pistol grip stock, and a US made detachable magazine to a stock SKS. Even though you've added only US parts, you've kicked it into 922(r) territory and probably have more than 10 imported parts remaining, therefore subject to the penalties if you were to somehow get caught with it.