Yes, in some cases, you can apply for a green card after entering the U.S. on the Visa Waiver Program (ESTA). This is generally possible if you are an immediate relative of a U.S. citizen (spouse, unmarried child under 21, or parent of a U.S. citizen over 21). In such situations, you may be eligible to adjust your status inside the U.S. without leaving, even though you entered on ESTA.