No. ESTA study use is not permitted for academic study or exchange programs in the United States.
ESTA is only for eligible travelers visiting the United States for tourism or certain short-term business purposes under the Visa Waiver Program, while study requires a student visa and exchange programs require the appropriate exchange visitor visa.
Therefore, if your purpose of travel is study or an exchange program, ESTA is not valid for that trip.
If you are planning travel to the United States, please confirm your travel purpose first and apply for ESTA only when it is eligible for your visit.