Jetpack social icons in other places on site

If you don’t want to rely on Jetpack for font awesome you need to have the CSS files loaded. Best way (in my opinion) to do this is via the CDN.
I use the following:

// Add font awesome & bootstrap
function awesome_css() {
    wp_enqueue_style("fontawesome", 'https://maxcdn.bootstrapcdn.com/font-awesome/4.5.0/css/font-awesome.min.css');
    wp_enqueue_style("bootstrap3", 'https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css');
    }
add_action( 'wp_enqueue_scripts', 'awesome_css' );

This goes into your functions.php file.

Then you have a few choices of how to add it. You can use the method you’ve referred to, or you can use the fontawesome cheat sheet

Refer to the examples on fontawesome for more info.