You will need to do the FAA "written" exam which is actually multi choice. This can be done at an approved centre in the UK. Flight Safety at Farnborough is one option. About 2 weeks studying will take care of that. Then you will need to do a flight test or "check ride" on your chosen aircraft with an FAA examiner.
Prior to this you need to get the FAA to verify your JAA license, google "license verification" and this should point you in the right direction. You then need to register under the alien flight student program with the USA TSA before commencing any tests or exams. A pain in the butt but it can be done.