The midfielder has signed a four-and-a-half-year deal with Gers after completing a £675,000 switch from Hamilton.
The 21-year-old joined his new team-mates for training for the first time on Friday and has already impressed his new boss.
Now Murty has tasked the Under-21 international to prove his potential can become reality by making the leap into the full Scotland squad.
The Gers boss said: “He adds physicality, a bit of legs, the ability to get box-to-box, he’s technically proficient, he has a range of passing.
“Typically in the past, outstanding Rangers midfield players have been internationals. Right now we have Ryan Jack who is an international and that is Greg’s challenge.
“His challenge is to become an international player while at Rangers and if he does that then he will be on the path to fulfilling some of his potential.
“But we’re just going to try to give him the stage to get as far as he can in the game. I’m sure he is going to do everything he possibly can to get himself the best chance.”
Murty confirmed Danny Wilson has undergone a medical with MLS side Colorado Rapids as he mulls over a move to the United States.
But he hopes Jack may return to action before the end of the season despite confirming he has been forced to undergo knee surgery.
Murty - who has had some good news after being told Ross McCrorie requires only rest and not an operation on his foot problem - said: “Ryan will be having surgery on his knee.
“It did not present that way initially but he will now be having surgery and will be out for an extended period.
“But it’s premature to say he will be out for the season.”