I haven't tried it myself, but I think so. I assume your FAA certificate was issued after 30 June 1945!
Attached is the guidance issued by the FAA in 2016. You might want to call them to confirm.
Also refer to this thread on another forum about avoiding the CAA £100 appointment fee:
https://forums.flyer.co.uk/viewtopic.php?f=1&t=107259