According to census records, his immigrant father was a resident alien (non-citizen) and his mother was American when Agnew was born. I don't know if he received citizenship later but the important fact is that he was not a citizen at Agnew's birth.
Interesting. Agnew was born on Nov. 9, 1918 (two days before the armistice) so he should be on the 1920 and 1930 censuses, both of which are now available to the public. Which one did you consult?