The fixture will take place in the week commencing 11 August with the game most likely to be on the Tuesday that week (12th) at the Liberty Stadium.
The Swans reached Round Two last season with a win over Walsall at home but succumbed to Premier League opposition in Reading in Round Two despite an impressive performance.
The full draw reads as follows: – Preston v Chesterfield, Chester v Leeds, Leicester v Stockport, Sheff Utd v Port Vale, Grimsby v Tranmere, Crewe v Barnsley, Hartlepool v Scunthorpe, Derby v Lincoln, Notts County v Doncaster, Sheff Wed v Rotherham, Shrewsbury v Carlisle, Wolves v Accrington, Bury v Burnley, Rochdale v Oldham, Nottm Forest v Morecambe, Huddersfield v Bradford, Macclesfield v Blackpool, Walsall v Darlington, Coventry v Aldershot, MK Dons v Norwich, Wycombe v Birmingham, Brighton v Barnet, Gillingham v Colchester, Southend v Cheltenham, Swansea v Brentford, Luton v Plymouth, Exeter v Southampton, Watford v Bristol Rovers, Bournemouth v Cardiff, Bristol City v Peterborough, Charlton v Yeovil, Millwall v Northampton, Swindon v QPR, Crystal Palace v Hereford, Dag & Red v Reading, Ipswich v Leyton Orient.