The Robins saw off Manchester United at Ashton Gate with a last-minute winner to earn a crack at the Premier League leaders.
The first leg will be at the Etihad Stadium on either 9/10 January with the return in Bristol on 23/24 January.
In the other semi, Chelsea face London neighbours Arsenal.
City have only faced Bristol City once in the League Cup, winning 2-1 at Ashton Gate in 2007 with goals from Emile Mpenza and Rolando Bianchi securing victory.over Gary Johnson’s side - now the Blues will take on Gary’s son Lee a decade later.
Of the 23 meetings in total, the Robins are ahead with 10 wins, six draws and seven losses against the Blues.
Johnson’s side have beaten Plymouth, Watford, Crystal Palace, Stoke and United to get this stage - their third League Cup semi-final appearance having made the same stage in 1970/71 and 1988/89.
Dates/ticket details will be confirmed in due course .
