When using icons in your UI, there are ways to help assistive technology either ignore or better understand Font Awesome.
If you're using an icon to add some extra decoration or branding, it does not need to be announced to users as they are navigating your site or app aurally. Additionally, if you're using an icon to visually re-emphasize or add styling to content already present in your HTML, it does not need to be repeated to an assistive technology-using user. You can make sure this is not read by adding the aria-hidden="true" to your Font Awesome markup.
If you're using an icon to convey meaning (rather than only as a decorative element), ensure that this meaning is also conveyed to assistive technologies. This goes for content you're abbreviating via icons as well as interactive controls (buttons, form elements, toggles, etc.). There are a few techniques to accomplish this:
If not representing an interactive element, like a button or link, use both a title attribute and an on the icon to provide a text alternative. This has the advantages of working with all modern screen readers, working well with the most ubiquitous speech recognition program, and helping users with cognitive disabilities by providing a mouse tooltip.
In addition to the recommendations above, use a title attribute which makes the accessible text discoverable by mouse and those with cognitive disabilities.