Manual:$wgFavicon

Details
The URL of the site favicon (the small icon displayed next to a URL in the address bar of a browser).

You do not need to set this if you upload your favicon.ico to the root of your site. That's where browsers look for it by default. Make sure file name is in lower case and its name is "favicon.ico".

To use a favicon located other than in your site root, in LocalSettings.php add $wgFavicon = "$wgScriptPath/path/to/your/favicon.ico"

Example:

Tip: The favicon image should be either 16 x 16 pixels or 32 x 32 pixels.