The 29-year-old's temporary deal at Prenton Park is due to expire in January.
Jennings started his career with Tranmere before spending part of last season with the League Two club.
"Steve is a hard-working midfielder with a superb work ethic and desire to win," manager Micky Adams is quoted as saying by BBC Sport.
Rovers continue their league campaign on Saturday at home to Stevenage.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Port Vale | 15 | 9 | 3 | 3 | 23 | 16 | 7 | 30 |
| 2 | Walsall | 14 | 8 | 3 | 3 | 27 | 15 | 12 | 27 |
| 3 | Notts County | 15 | 7 | 6 | 2 | 23 | 13 | 10 | 27 |
| 4 | Doncaster RoversDoncaster | 15 | 8 | 3 | 4 | 21 | 17 | 4 | 27 |
| 5 | Crewe AlexandraCrewe | 14 | 7 | 4 | 3 | 17 | 13 | 4 | 25 |
| 6 | MK Dons | 15 | 7 | 3 | 5 | 24 | 17 | 7 | 24 |
| 7 | Grimsby Town | 15 | 8 | 0 | 7 | 19 | 25 | -6 | 24 |
| 8 | Gillingham | 15 | 7 | 2 | 6 | 16 | 12 | 4 | 23 |
| 9 | Chesterfield | 15 | 5 | 7 | 3 | 28 | 18 | 10 | 22 |
| 10 | Bradford CityBradford | 15 | 6 | 4 | 5 | 20 | 16 | 4 | 22 |
| 11 | BarrowBarrow | 15 | 6 | 4 | 5 | 16 | 12 | 4 | 22 |
| 12 | Fleetwood TownFleetwood | 14 | 5 | 6 | 3 | 20 | 15 | 5 | 21 |
| 13 | Salford City | 15 | 5 | 5 | 5 | 14 | 17 | -3 | 20 |
| 14 | AFC Wimbledon | 12 | 6 | 1 | 5 | 18 | 10 | 8 | 19 |
| 15 | Newport CountyNewport | 15 | 6 | 1 | 8 | 19 | 26 | -7 | 19 |
| 16 | Cheltenham TownCheltenham | 15 | 5 | 3 | 7 | 19 | 22 | -3 | 18 |
| 17 | Tranmere RoversTranmere | 14 | 4 | 5 | 5 | 10 | 17 | -7 | 17 |
| 18 | Accrington StanleyAccrington | 14 | 4 | 4 | 6 | 18 | 22 | -4 | 16 |
| 19 | Bromley | 14 | 3 | 6 | 5 | 16 | 18 | -2 | 15 |
| 20 | Harrogate TownHarrogate | 15 | 4 | 3 | 8 | 12 | 21 | -9 | 15 |
| 21 | Colchester UnitedColchester | 14 | 2 | 7 | 5 | 17 | 21 | -4 | 13 |
| 22 | Swindon TownSwindon | 15 | 2 | 6 | 7 | 16 | 23 | -7 | 12 |
| 23 | Carlisle UnitedCarlisle | 15 | 3 | 2 | 10 | 13 | 28 | -15 | 11 |
| 24 | Morecambe | 15 | 2 | 4 | 9 | 14 | 26 | -12 | 10 |
| > League Two Full Table | |||||||||
