No, its not common, using it as provoking someone is much more common and definitely older use as well. This was the first time I've ever seen it being used like this and I've been in daily contact with English since 2010
There is an example of it being used in the way I am saying in the first 20 seconds of this video:
View: https://www.youtube.com/watch?v=liLU2tEz7KY
And I also posted a link with the way its more commonly used
https://idioms.thefreedictionary.com/fucks+with+you
The only place I've ever seen it being used as hanging out with someone is in this thread, I even thought it was a typo and he mean't "not fuck with me".