Yes, since your parents are immediate relatives, you should be able to adjust their status. I had a client who is an American citizen who adjusted the status of her Austrian mother last month. She entered the U.S. under the Visa Waiver Program. You should consult with an experienced immigration attorney like me or someone else to help you with this application. Do not try to file it on your own.
This response is provided for informational purposes only. It is not legal advice and does not create an attorney-client relationship. Questions and answers posted to this forum are public and cannot be kept confidential. Although admitted in DC, I currently reside in Texas and I am authorized to practice U.S. immigration law worldwide..