It is common practice to allow users to set a “signature” that is displayed at the bottom of every forum post or reply that they add.
This can be text, and optionally, an image.
Once activated, the user can set their forum signature via their Edit Profile screen:
The user can also remove a previously uploaded image and change their signature.
Note that any URL entered is automatically shown as a hyperlink, so the above would appear as:
Provided in the Extensions Plugin.