Well there you go. That’s my learnin’ for the day.

Craig Ferguson of TV fame, or notoriety, said that in Scotland a soft drink was called ‘’a ginger’’. Does this group agree?

Wiktionary.org has an article on Scottish slang that confirms this (ginger is, among other things, scottish slang for a carbonated beverage).  I found the same thing on a few other websites on Scottish slang, including http://www.firstfoot.com. So this seems to be true (but, of course, I would defer to a native of Scotland!).  My WAG would be that the term is derived from ginger ale and then broadened to mean any carbonated drink.

DSL:

GINGER, n. Add: 3. A fizzy soft drink (of any flavour) (Edb., Gsw., Ayr., Dmf. 2000s).
*Gsw. 1984 James Kelman The Busconductor Hines 32:
   Christ sake man, transistor radios playing, drinking bottles of ginger, the place stowed out with folk chatting about football and everything.
*Gsw. 1985 Michael Munro The Patter 29:
   ginger A general term for all varieties of fizzy soft drinks: ‘Gie’s a boatle a ginger, missis,’ ‘What kinna ginger, son?’ ‘Lemonade.’
*Gsw. 1989:
   Get us a boattle o ginger when ye’re doon it the shoap — American cream soda.
*Gsw. 1990 Alan Spence The Magic Flute (1991) 18:
   ‘Can I finish that ginger?’ he said, pointing at a cola bottle, almost empty, on the sideboard.
*m.Lth. 1992:
   I always asked for ginger even before yer granma came on the scene.
*Gsw. 1993 Herald 12 Mar :
   We asked the nice French waitress what kind of ginger it was. “Fresh ginger,” she said. We said that we assumed it was a fresh bottle of ginger but was it cream soda, limeade, Irn Bru or what?
*m.Sc. 1994 Martin Bowman and Bill Findlay Forever Yours, Marie-Lou 36:
   It’s true ah shouldnae drink...But what the fuck else pleasure dae ah hiv left in ma life? Nae wey ah’m gauntae the bar jist tae drink ginger!
*Gsw. 1998 Herald 11 Jul 26:
   You do not equate the French with TV dinners, microwaves, bottles of ginger and fish suppers.
*Sc. 1999 Herald 30 Sep 9:
   Head brewer Robin Graham said: “In Glasgow, before the war, all the shops used to brew their own ginger beer. That’s why you still get wee boys going in for a bottle of lemonade and asking for a bottle of ginger.”

I agree it’s likely to be short for “ginger ale” or “ginger beer.”