Hi Robert,

Only way to show Social Icons on Header to at them as part of Menu Item, see the example:

You can add social network icons in this form:

<i class="fa fa-{icon-name}"></i> where {icon-name} is the icon from font awesome collection which can be found here:

https://fontawesome.com/v4.7.0/icons/

Here is how to find the icon name:

(view large version)

Please don't forget to tick this option:

(view on new page)

Then add it to menu item in Appearance > Menus

(view large version)

Have a nice day!