To use any other icon font other than the Genericons, you would need to load that font into your site, either by coding it in, or by a plugin. I would recommend the plugin method which offers font awesome.
If you need this icon, you will have to load the Font Awesome font into the theme, which can be done through a child theme or a plugin. You will then need to create a new CSS style for this icon and do it in a way that it works like this theme’s Genericons are coded. The styling for the social icons is found in the theme’s style.css around line 1918. I would recommend you see how it was done there, then you will need to add to it or change the social icons to use the Font Awesome font instead of Genericons. This also means you would need to change each of the social networks icon css to use the content “” icon code from font awesome. For example, the facebook CSS uses this:
.social-navigation a[href*="facebook.com"]:before {
content: "\f204";
}
So for font awesome, I think it would be this:
.social-navigation a[href*="facebook.com"]:before {
content: "\f082";
}
How you load the font-awesome font, will be up to you, but check out the plugins first. The other option would be to included the actual font in your theme from the actual Font Awesome website in your theme. Here is some info:
Add Font Awesome
If you do it manually like that, then you should use a child theme method for WordPress.
I wish this could be done easy with a couple mouse clicks, but for the change you want, you have some work to do.