Yes, an adopted child can potentially become a U.S. citizen even though the child is not biologically related to you. U.S. citizenship law provides specific routes for qualifying adopted children of U.S. citizens.
However, adoption by an American citizen does not automatically make every child a U.S. citizen in every situation. The result depends on factors such as the child's age, whether the adoption meets U.S. immigration-law requirements, where the child lives, and whether the U.S. citizen parent meets applicable residency or physical-presence requirements.
So in your Germany example, the lack of a biological relationship would not itself prevent the child from obtaining U.S. citizenship, but the adoption and citizenship process would have to satisfy the applicable U.S. legal requirements.
