Rein, guys, rein
I would say:
He wants to be given free rein to do things his way.
If horses would be kings!
Arein is used to control. A reign is what a king's time ruling is called.
The result of this poll goes to show that a lot of people just repeat phrases they hear without thinking about what the phrases mean, or how they came to be.
Having said that, I suppose both could be made to work... just.
It is rein, not reign. Ignore the majority.
This makes me sad, that so many people on this website would choose the g option. A rider loosens the reins on a horse to ease up on control of its movements. – to give it more freedom. Giving free rein has nothing to do with ruling a kingdom.