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  add  

Example:

One icon file can contain multiple images with different resolutions each. This is also what is recommended for the favicon. An icon file with 16 x 16 pixels, 32 x 32 pixels, 48 x 48 pixels and 64 x 64 pixels will display well on most devices and so is a good choice. The single images can be compressed; should the resulting icon file become bigger than 50 kb anyway, the highest resolution can be left away!