ESTA must be applied for using the passport that will be used to enter the United States.
In other words, even if you hold multiple nationalities or passports, you must enter the information of the passport you will actually use to enter the United States when applying for ESTA.
* Visa Waiver Program (VWP) passport holders
ESTA can be applied for with that passport, and after approval, entry must be made using the same passport.
* Non-Visa Waiver Program (VWP) passport holders
ESTA cannot be used, and you must obtain a U.S. visa (such as B1/B2).