The Font Awesome icon shortcode has 3 options:

Icon: Choose the icon
Example: [fa icon="fas fa-cog"]

Href: Add a URL to the icon
Example: [fa href="URL"]

Target: Link the button to a new window, or not. To link in the same use _self or new _blank window
Example: [fa target="_self"]

On the Font Awesome website you can see all available font classes you can use.