The Giants will travel to Glasgow on October 14 attempting to progress into the quarter final stages of the competition.
Meanwhile Cheshire Jets will travel to face Sheffield Sharks, while neighbours Mersey Tigers will host Surrey Heat. Both matches will take place on October 12.
London Lions will host Durham Wildcats in the first BBL Cup match of the season on October 7.
Newcastle Eagles, Plymouth Raiders, Leicester Riders and Worcester Wolves all automatically progress into the quarter finals by virtue of higher league positions last season.
Full BBL Cup first round draw
7 October 2012: London Lions v Durham Wildcats
12 October 2012: Mersey Tigers v Surrey Heat
12 October 2012: One Health Sharks Sheffield v Cheshire Jets
14 October 2012: Glasgow Rocks v Manchester Giants
BBL Cup quarter final draw
Game 1 – Tigers or Heat v Raiders
Game 2 – Sharks or Jets v Rocks or Giants
Game 3 – Eagles v Wolves
Game 4 – Lions or Wildcats v Riders