Cardiff are one of the seeded teams in the Southern half of the draw which takes place at 7am, Tuesday 28th June.
The 36 teams that progress into round two will be joined by the 12 Premiership teams who are not competing in Europe.
There will be 24 winners in round two who will then team up with the 8 Premiership teams that are in Europe making 32 teams in round 3.
As a seeded team Cardiff will face any one of the following 18 unseeded teams in round 1.
Walsall, Colchester, Milton Keynes, Yeovil, Swansea, Southend, Torquay, Peterborough, Northampton, Wycombe, Leyton Orient, Bristol Rovers, Cheltenham, Oxford, Notts County, Shrewsbury, Rushden or Barnet.