You can add additional ratings to your US certificate issued on the basis of a foreign license.
From the FAA's website:
The holder of a U.S. pilot certificate issued under FAR 61.75 can qualify and be tested for additional ratings by complying with all of the U.S. certification requirements for that particular rating. These additional ratings will be added to the holders certificate with a notation in parenthesis, "US Test Passed".
If you want to get an IR issued in the US on the basis of a JAR one you need to take a computer-based theory exam in the US.