I have no Facebook account, no Twitter account, nothing. Would a girl be concerned about this if she found out? I really want a girlfriend and never had one before but if she knows my non-existent social media life, I think she would avoid me...
A girl will not be turned off if you are not active in social media. However, you will make yourself more difficult for her to contact you. On the other hand, there will be much less options for you to contact her.
Is there a reason why you do not have any social media account?
I would think rather the opposite, if anything. I don't think she would care but maybe she would think it was cool or interesting since almost everyone is involved. I think a girl who isn't involved in social media would be pretty interesting, but that's just me :)