Update: As of 2024, Facebook automatically add the @ (at) symbol on your YouTube handle. This tutorial is not needed anymore.
This post is archived for future reference.
On Facebook, adding your YouTube handle does not work, as Facebook will remove the @ (at) symbol. YouTube links without the @ symbol only works if you have custom URL.
To make YouTube handles work on Facebook, you need to add the + (plus) sign on it1, so instead of @AnimMouse, it should be +@AnimMouse.
This will prevent Facebook from removing the @ sign and allows your Facebook viewers to click the link to view your YouTube channel.