You can order a short-barreled upper. In and of itself, the upper is just an accessory. It becomes an NFA weapon when you attach it to a lower. At that point, you're manufacturing an NFA item, for which you need approval.
Basically, it comes down to this:
- Download and print out two copies of the ATF Form 1 [pdf]
- Download and print two copies of the Certificate of Compliance [pdf]
- Fill out the relevant parts
- Get two passport photos
- Take the paperwork and a $200 check to your local sheriff.
- Have them take fingerprints and send it all off.
- Wait. Then wait some more.
In the meantime, you'll need to get the lower receiver engraved with your name, city and state. Once the Form 1 comes back approved, you can assemble the rifle.
Now, there's some question as to whether it's wise to have the short-barreled upper before you get approval. If you're found to be in possession of it at the same time you have a lower, constructive possession could be implied, and that could lead to trouble.
As such, it's a good idea to get approval before buying the upper, or to store the upper in a different location than the lower.