[californian by choice]

And he didn’t say when he took the oath of citizenship?

[Harmless Teddy Bear]

Actually I don't believe he would have had to since he was formally adopted by American citizens.

A child who immigrates to the United States as the adopted child of a U.S. citizen automatically becomes a U.S. citizen if the adoption is full and final before the child's 18th birthday, if the child is "lawfully admitted" as a permanent resident before his or her 18th birthday, and if he or she "is residing" in the United States in the citizen parent's legal and physical custody before his or her 18th birthday.

While Superman did not enter the country as a prospective adoptive child he was legally adopted by the Kents who are American citizens.

Once the Adoption was complete he became a US citizen without needing to go through a nationalization process or swear any oaths.