A car should be imported by a Registered Importer. They will have to
petition and possibly modify the car to comply to the Federal Safety Theft
Bumper and Theft Prevention Standards.
A list of Registered Importers can be found here, here and here.
Examples of cars being imported to the USA.
I've picked some Ferrari's and one Ford Escort RS Cosworth.
All Ferrari's are also available as a US-model, therefore making it slightly easier to import one. One Ferrari 412 was denied, because the Registered Importer (G&K) was too late supplying the crash-test documents. Also note that Fiat R&D USA has some comments in some docs, against importing a car.
On the other hand, the Escort RS isn't available as a US-model, and had to go through some modifications. The document refers to the Federal Motor Vehicle Safety Standards (49 CFR 571). Most of them can be found here, and a Table of Contents of all standards is here.
As a bonus, I included something about Bugatti too...
This document (49 CFR 591) describes the Federal Safety Bumper and Theft Prevention Standards: on what grounds a car can be imported.
This document (49 CFR 592) lists the procedures and duties for the Registered Importers.
This document (49 CFR 593) list the procedures that determine if a car may be imported. It also shows a list of cars that already may be imported. You will find that most imported cars also come as a US model, except for the Citroen XM, Ford Escort RS, some Mercedes Benz utility vehicles (Geländewagen) and horse trailers. The barchetta should be in this class too.
Don't pay too much to your Registered Importer. Here are the fees listed (49 CFR 594).
My list of required barchetta alterations.
Motor Vehicles and the 1990 Clean Air Act can give you
a hint about smog standards
Importing a car, a how-to docs by the US Customs.
List Of Nonconforming Vehicles Decided To Be Eligible For Importation As Of January 13, 1997, a list similar to 49 CFR 593
Know before you go