This will all depend on the version of Moodle your organization is currently using, and Moodle has all the necessary Bootstrap CSS as well as FontAwesome Fonts & CSS.
You cannot add the kind of HTML you are wanting to add as it is not allowed.
However, what you are trying to do can be achieved by just adding some simple HTML.
For example: Using the Text Editor in Moodle be it in a Course of on the Frontpage and adding this code (see below)
<a class="btn btn-primary btn-lg" href="#" role="button"><i class="fa fa-home"></i> Learn more »</a>Learn more »
Which means you can add FontAwesome icons in Moodle provided the version is Moodle 3.3 onwards.
Hope this helps?