The ICAO does not issue pilots licences. Most countries including the USA are members of the ICAO.
From the ICAO website
ICAO does not issue any licences. Licences issued by ICAO Contracting States on the basis of Standards and Recommended Practices of Annex 1 – Personnel Licensing, are habitually called ICAO licences. This has led many to believe that there is a specific ICAO or international licence. The fact is that there is not one single international licence issued by ICAO or any other organization. States issue their own licences based on national regulations in conformity with Annex 1 specifications and validate licences issued by other Contracting States on the basis of bilateral or multilateral agreements or the fulfilment of nationally legislated requirements.