The tiddler title needs to be $:/favicon.ico, but the content doesn't need to be in .ico format.
If you put an image file into a tiddler and then rename the tiddler to $:/favicon.ico so far it has worked for me with jpg, png and gif images. I haven't gotten svg to work yet but I think that is a browser issue, not a tiddlywiki issue. The only other limit I have run into is that it can't be a _canonical_uri tiddler -- You received this message because you are subscribed to the Google Groups "TiddlyWiki" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/tiddlywiki. To view this discussion on the web visit https://groups.google.com/d/msgid/tiddlywiki/15cf3f8a-8abb-4c9b-bf3f-fabd7bc061a2%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.

