Swiss-born Gjokaj, who joined the Rams in the summer on a two-year deal, will remain at Brunton Park until just after the New Year.
The 19-year-old made his debut for Nigel Clough's side as a late substitute in the 2-2 home draw with Sheffield Wednesday on the opening day of the Championship season, and that remains his only first-team outing for them.
"He's another young lad who will come in and give us options at a time when we are looking for depth in our squad," said Carlisle manager Greg Abbott.
"Hopefully he will benefit from his time here and he will give us an extra bit of cover and competition that we need."
Gjokaj will team up with the Cumbrians ahead of their league fixture at Yeovil this weekend.