The 21-year-old had been on loan at Northampton Town, until that deal finished earlier this month.
Archer has been capped 14 times for Scotland's Under-21 side and he has also had spells at Bishop's Stortford and Wycombe Wanderers.
He has become the second player to join the Lions today, with Michael Tonge arriving from Leeds United for the remainder of the campaign.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| C | Manchester CityMan City | 38 | 28 | 7 | 3 | 96 | 34 | 62 | 91 |
| 2 | Arsenal | 38 | 28 | 5 | 5 | 91 | 29 | 62 | 89 |
| 3 | Liverpool | 38 | 24 | 10 | 4 | 86 | 41 | 45 | 82 |
| 4 | Aston Villa | 38 | 20 | 8 | 10 | 76 | 61 | 15 | 68 |
| 5 | Tottenham HotspurSpurs | 38 | 20 | 6 | 12 | 74 | 61 | 13 | 66 |
| 6 | Chelsea | 38 | 18 | 9 | 11 | 77 | 63 | 14 | 63 |
| 7 | Newcastle UnitedNewcastle | 38 | 18 | 6 | 14 | 85 | 62 | 23 | 60 |
| 8 | Manchester UnitedMan Utd | 38 | 18 | 6 | 14 | 57 | 58 | -1 | 60 |
| 9 | West Ham UnitedWest Ham | 38 | 14 | 10 | 14 | 60 | 74 | -14 | 52 |
| 10 | Crystal Palace | 38 | 13 | 10 | 15 | 57 | 58 | -1 | 49 |
| 11 | Brighton & Hove AlbionBrighton | 38 | 12 | 12 | 14 | 55 | 62 | -7 | 48 |
| 12 | Bournemouth | 38 | 13 | 9 | 16 | 54 | 67 | -13 | 48 |
| 13 | Fulham | 38 | 13 | 8 | 17 | 55 | 61 | -6 | 47 |
| 14 | Wolverhampton WanderersWolves | 38 | 13 | 7 | 18 | 50 | 65 | -15 | 46 |
| 15 | Everton | 38 | 13 | 9 | 16 | 40 | 51 | -11 | 40 |
| 16 | Brentford | 38 | 10 | 9 | 19 | 56 | 65 | -9 | 39 |
| 17 | Nottingham ForestNott'm Forest | 38 | 9 | 9 | 20 | 49 | 67 | -18 | 32 |
| R | Luton TownLuton | 38 | 6 | 8 | 24 | 52 | 85 | -33 | 26 |
| R | Burnley | 38 | 5 | 9 | 24 | 41 | 78 | -37 | 24 |
| R | Sheffield UnitedSheff Utd | 38 | 3 | 7 | 28 | 35 | 104 | -69 | 16 |
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