"If you can have her" by itself could mean a lot of different things. In this example you've given "If you can have her give me a call as soon as she can." means "Please tell her to call me as soon as she can." It's just another way of asking someone to tell someone else to do something.

"If you can have her" means "please ask her".... to call me as soon as possible.

It's an incomplete sentence, but people understand: If you can have her give me a call (= get her to call me), that would be great. :)

To have or get something done. Means not to do it yourself, but someone else does it for you for free or for a fee. "I have my hair cut every three months" ... I go to the hairdresser and she cuts it. "I cut my hair every three months" .... I cut my own hair (UGH what a mess!)