Archer, 19, has impressed since arriving on loan from Tottenham Hotspur in the final week of September.
The Scotland U21 international has appeared 12 times between the sticks for the Blues, keeping three clean sheets in the process.
Ainsworth told wwfc.com: “We’re really pleased with the way Jordan’s settled into the squad and his level of performance.
“He’s made his professional debut and is gaining valuable experience of playing first-team football.
“I’d like to thank Tottenham for allowing us to keep Jordan for the rest of the season, we are very grateful.”