Depends.
IF you have a freestanding FAA license you will need an FAA medical;
IF you have an FAA license issued on the basis of another ICAO licence you can use that FAA license with an FAA medical or with a medical that makes that ICAO licence valid.
Chapter and verse
§ 61.75 Private pilot certificate issued on the basis of a foreign pilot license.
(a) General. A person who holds a current foreign pilot license issued by a contracting State to the Convention on International Civil Aviation may apply for and be issued a private pilot certificate with the appropriate ratings when the application is based on the foreign pilot license that meets the requirements of this section.
(b) Certificate issued. A U.S. private pilot certificate that is issued under this section shall specify the person's foreign license number and country of issuance. A person who holds a current foreign pilot license issued by a contracting State to the Convention on International Civil Aviation may be issued a private pilot certificate based on the foreign pilot license without any further showing of proficiency, provided the applicant:
(1) Meets the requirements of this section;
(2) Holds a foreign pilot license that—
(i) Is not under an order of revocation or suspension by the foreign country that issued the foreign pilot license; and
(ii) Does not contain an endorsement stating that the applicant has not met all of the standards of ICAO for that license;
(3) Does not currently hold a U.S. pilot certificate;
(4) Holds a current medical certificate issued under part 67 of this chapter or a current medical certificate issued by the country that issued the person's foreign pilot license; and
(5) Is able to read, speak, write, and understand the English language. If the applicant is unable to meet one of these requirements due to medical reasons, then the Administrator may place such operating limitations on that applicant's pilot certificate as are necessary for the safe operation of the aircraft.
(c) Aircraft ratings issued. Aircraft ratings listed on a person's foreign pilot license, in addition to any issued after testing under the provisions of this part, may be placed on that person's U.S. pilot certificate.
etc..............