We’ve used default WordPress menu options to add Social icons. If you’re familiar with “WORDPRESS” menu options then its relatively easy task for you.
To create a custom menu is actually really simple.
1. Login to the WordPress Dashboard.
2. From the ‘Appearance’ menu on the left-hand side of the Dashboard, select the ‘Menus’ option to bring up the Menu Editor.
3. Select Create a new menu at the top of the page
4. Enter a name for your new menu in the Menu Name box
5. Click the Create Menu button.
After the menu has been created You’ve to add social site URL and Link Text from Custom Links sections and click OK:

Important: Please add full URL (e.g http://www.facebook.com/username) for site URL on Custom Links sections.