Download the font awesome and then move the folder to your theme folder.

Here are the two methods of adding font awesome inside our drupal site.

Method 1:

Then add 'stylesheets[all][] = font-awesome/css/font-awesome.min.css' to the stylesheets included in the .info file.

Method 2:

Write the below function in your template.php file.

function Your-theme_preprocess_html(&$vars) {
  $filepath = path_to_theme() . '/font-awesome/css/font-awesome.min.css';
  drupal_add_css($filepath, array(
  'group' => CSS_THEME,
  ));
}

Then You can use font awesome inside your site wherever you want.