In the Style Designer, create a new Character Style that will represent the Font Awesome bullet.

In the Character Style Options, under Additional CSS Classes, add fa, a whitespace, and the class of the icon you want to use. (For example: fa fa-warning) For a reference of all the icons available, refer to the Font Awesome Cheatsheet at:

Select the Paragraph Style that is to have the bullet added.

In the Bullet Properties area for the Paragraph Style, under the Property called Character Style, select the name of the Character Style that has the Font Awesome icon applied to it.

(Optional) If the Paragraph Style was initially an unordered list in the source document, it is also necessary to add a single whitespace to the Bullet Property called Text so the default bullet does not emit from the source document.