It is listed as such in wiki, however my literature never refers to it as such. My gut tells me to follow papers and monographs on the matter, but my concern is that I will make an easily avoidable mistake, or that I simply misunderstood the text.
One of my first Google hits is a widely-cited article:
Eberhart, Russell C., and Yuhui Shi. "Comparison between genetic algorithms and particle swarm optimization." In International Conference on Evolutionary Programming, pp. 611-616. Springer, Berlin, Heidelberg, 1998.
The third paragraph of the article says:
Regardless of the specific implementation, it is generally agreed that GAs utilize one form or another of three operators: selection, crossover, and mutation.
There's no authorized body to pronounce the truth on this sort of thing. Personally, I would say it absolutely is a genetic operator. Someone else might disagree. I don't thing either is objectively wrong or makes one look amateurish or silly.