No. A round-trip ticket is not always required, but travelers entering the United States with ESTA may need to show a ticket for departure from the United States.
This means that it does not have to be a round-trip ticket back to your home country.
A ticket from the United States to another country may also be accepted.
The important point is whether you can show that you plan to leave the United States after your stay.
If you only have a one-way ticket, it may cause issues during the entry process, so it is better to prepare proof of onward or return travel.