No. ESTA internship or part-time work is not permitted 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, and it cannot be used for employment or regular work activities.
Therefore, if your purpose of travel is part-time work or an internship, 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 valid for your visit.