Center calls the cadence
 

Do we have a rule in NF, that the center cannot call the cadence?

Nope. Should there be?
Can't say as I've been at a game where it was done, but I have heard of it.
I see nothing wrong.

There's no requirement that there even be a cadence, much less who can do it.

I have seen the snapper call cadence on punts.

I once played on a team where the QB had laryngitis and could not talk. Subs were bringing throat spray on and off the field. The center did the cadence the whole game.