Word Choice

The first is more succinct.

Putting that aside, I'd rather write it as, I asked her to give you a call too.


Ending the sentence with also gives it an uncomfortable sound.

If you asked her to give you a call, you asked her directly, e.g. you said "give him a call".

If you asked for her to give you a call, you asked someone else (a third person) to arrange for her to give him a call, e.g. you said "please ask her to give him a call".