My favori site for icones is Iconomize.com because the icone toi choose automatically installs to your desktop with the shortcut already set. They have the Facebook icone here, link Just click to install and it goes right on the desktop.
In fact yes toi can:First toi go in Google images and type "FACEBOOK ICONS"and save the pic,then toi go and search"www.iconverticons.com",convert the pic into an icone and download it,then go in the desktop: go to"new","shortcut",type:"www.facebook.com",then name it "Facebook",then right click on the shortcut ,go to properties,change icone and choose the one toi converted before,then press APPLY.and then it should come perfect