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