Cricketer,
1) If you already have a 61.75 certificate (ie issued on the basis of your foreign JAA licence) then I think you need to:
a) complete the new foreign licence verification procedure for a future rating/certificate issue at your nominated FSDO
b) sit and pass a reduced IR written knowledge exam - the IR Foreign Pilot test
c) visit said FSDO with your verification letter and JAA licence and test results and have them undertake the necessary administrative update to your 61.75 licence.
Note that your JAA licence must be valid and your IR must be current from verification request through to administrative update.
2) Alternatively, you could sit the full written and pass the normal IFR rating practical test (assuming you already meet all the experience requirements of 14 CFAR 61.65 by virtue of your JAA IR training and flying). Then your 61.75 certificate will also be endorsed with "US Test Passed".
3) If you already have a standard FAA certificate (ie you originally undertook a course of training, a full written test and an FAA flight test) then you can certainly do the second above on your standard certificate without the endorsement; whether the first is allowed I don't know.
4) If you have neither FAA licence (standard or 61.75) then you have to get one of them first!
BTW, don't quote me - I'm not a CFI, lawyer or holder of either IR. I have found the New York IFO very helpful on answers not obvious in the FAR/AIM. Don't ask the FAA office in London (Gatwick?) - they have no operations inspectors and will refer you to New York IFO or another FSDO.