Manual:$wgFavicon

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

Upload your favicon.ico to the root of your domain/subdomain, make sure file name is in lower case and its name is favicon.ico

Alternatively edit the $wgFavicon setting in LocalSettings.php and 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.