See the American Board of Otolaryngology website re: information for foreign trained surgeons at:
http://aboto.org/BOI.htm#pri
In short, it is possible to be a foreign trained ENT and get US board certification, but there are VERY specific requirements, and it appears that only senior surgeons from certain countries can meet these requirements. These are (and this is cut & paste from the website):
FOREIGN TRAINING
An applicant who entered otolaryngologic training in the United Kingdom or the Republic of Ireland prior to July 1, 2000 in a program accredited by the Specialist Advisory Committee, and who received a certificate of accreditation in otolaryngology from the Joint Committee on Higher Surgical Training in the United Kingdom or the Republic of Ireland may be considered for examination.
An applicant who entered otolaryngologic training under the New Zealand program after January 1, 1984 but before July 1, 2000 and who passed the examination leading to Fellowship in the Royal Australasian College of Surgeons may be considered for examination.
An applicant who entered otolaryngologic training under the Australian program after January 1, 1986 but before July 1, 2000 and who passed the examination leading to Fellowship in the Royal Australasian College of Surgeons may be considered for examination.
Individuals who entered otolaryngologic training in Canadian programs prior to July 1, 2000 may be considered for examination.