Formal, legal adoption wasn’t common in the U.S. until the late 1800s. (State adoption laws didn’t even exist until after Massachusetts passed the first one in 1851.) Before that, if mom and dad couldn’t take care of a child, a relative, neighbor or friend took that child in, or the child was sent to a county orphanage or poor home. In even earlier days, orphaned or poverty-stricken children were also sold by their towns into indentures.
The Adoption History Project at the University of Oregon has a great timeline of adoption history in the U.S. Check it out to see what was going on when your family member was adopted.
To learn more about adoption and genealogy research, check out these links: