The young City player joins up with his new team mates on Thursday for a one month loan spell.
Farrah has made just one apparance for the first team this season. That was in the 3 - 1 win at Oxford in the Carling Cup.
Cardiff have now loaned out four players.
Nat Jarvis - Newport County
Dekel Keinan - Crystal Palace
Jon Parkin - Huddersfield Town
Ibby Farrah - Tamworth.
Malky Mackay is trying to get a player in before the loan windown closes.