Google Analytics is for web traffic statistics. How many visitors, which pages did they view, where are they from, how long were they on a page etc...
It cannot be used to work with email.
This company is one of the best and they can assist with the social media tie-in as well.
Email Marketing Solutions from Constant Contact
Although something tells me we might have a spammer on our hands. Don't tell me let me guess: in a few days you will reply "Oh I found someone! Check it out! LINK".