Non-US citizens can drive up to one-year on their foreign country license as long as that country is a part of the Geneva Compact. To find out if your home country is part of the Geneva Compact, please check: http://transportation.ky.gov/Driver-Licensing/Documents/Geneva_Compact_Countries.pdf
The one-year date comes from the entry date stamped on their immigration document such as the I-94.
If from a country that is not recognized by the Geneva Compact the non-US citizen cannot drive on their foreign license.
Applications for a Kentucky drivers license can be made at the address below:
The Department of Motor Vehicles (DMV)
162 E Main Street, 2nd Floor, Room 230
Downtown Lexington, KY
Phone numbers are 859-246-2153 or 859-246-2154.
The following information is required at the time of application:
KRS 186.412 requires all non U.S. citizens wishing to apply for a Kentucky driver's license or ID card to make application to a Division of Driver Licensing Regional Office. For more information about the rules for obtaining a Kentucky Driver’s License, please go to: http://transportation.ky.gov/driver-licensing/pages/non-us-citizens.aspx