It's hard to pin down who first made this remark because it is a corollary of the very basic fact that if $\sigma$ is an automorphism of the cyclotomic field $Q_{|G|}$, then there exists an integer $m$ coprime to $|G|$ such that for every character $\chi$ of $G$, we have $\chi(x)^\sigma = \chi(x^m)$. The earliest explicit reference I can find is in Huppert's book Enliche Gruppen I in 1967. It appears there as Satz V 13.7 (b), on page 537.

It's hard to pin down who first made this remark because it is a corollary of the very basic fact that if $\sigma$ is an automorphism of the cyclotomic field $Q_{|G|}$, then there exists an integer $m$ coprime to $|G|$ such that for every character $\chi$ of $G$, we have $\chi(x)^\sigma = \chi(x^m)$. The earliest explicit reference I can find is in Huppert's book Endliche Gruppen I in 1967. It appears there as Satz V 13.7 (b), on page 537.