Upvote:3
Visa holders do not need to apply for ESTA to travel to the US for the purpose of their visa.
If you intend to travel to the US for a different purpose than the one permitted by your visa, i.e. you want to go on a holiday but not start your exchange program, then you need to apply for ESTA to travel under the Visa Waiver Program. (But if you do that, as I understand it, you have to exit and re-enter the US to change to J-1 status.)