There are two circumstances under which U.S. citizens may adopt a child from another country and get that child a green card. One is when the child is an orphan. The other is when the child is under the age of 16 and has lived in the petitioning parents’ legal custody for two years before submitting the green card application.
Because of various legal technical requirements, international adoption is not a realistic option for parents who are U.S. lawful permanent resident (green card holders). Nor is it a way to help someone over age 16 gain U.S. lawful permanent residence (a green card).