Well, pretty much anything can be given a US airworthiness certificate provided it's not literally falling to pieces. You could certificate such an aircraft as a Special Airworthiness Certificate in the Experimental category -- Specifically one of:
Experimental -- Research and Development
To conduct aircraft operations as a matter of research or to determine if an idea warrants further development. Typical uses for this certificate include new equipment installations, operating techniques, or new uses for aircraft.
Experimental -- Showing compliance with regulations
To show compliance to the airworthiness regulations when an applicant has revised the type certificate design data or has applied for a supplemental type certificate or field approval.
If your goal is to ultimately get this aircraft a Standard airworthiness certificate you would probably want the latter, to allow you to conduct test/certification flights in the modified aircraft.
To then get a standard airworthiness certificate things are a bit more murky. You could get a US STC based on the European STC & using this aircraft as the example for conformity inspections and flight testing, but that would require going through the STC process.
The other option would be the 337 process, in which case you are also going to need an A&P mechanic (preferably one with Inspection Authorization) and the cooperation of your local FSDO to approve the modification as a "major alteration" (FAA Form 337 - Instructions here).
As you alluded to in your question, something like installing a Rotax engine in a Cessna 150 is a "Major Modification" that has no "FAA Approved Data" (STC procedure/drawings/etc.) to include with the 337, so you would need to submit "Acceptable Data" for your modification (the European STC is a good starting point) and work with the FAA to obtain approval for the modification.
This is something you would want to talk to the FAA about before purchasing an aircraft with such a modification (there's a good chance they may not approve the modification, which would leave you with an unairworthy aircraft, or one restricted to the Experimental category).