The short answer is yes. In Pennsylvania one adult can adopt another adult. An adult adoption is the adoption of any individual who is at least 18 years old. Perhaps the more interesting and important question is, "why would someone want to adopt an adult?"
In 2003, the Pennsylvania Department of Health issued a set of procedures known as the "Assisted Conception Birth Registration". It is a set of procedures for the issuing of birth certificates for children conceived through assisted reproduction that lists the intended parents as the child's parents (rather than a surrogate). The procedure is an alternate method to adoption that allows the intended parents to establish legal parentage.