Martinez has been especially pleased with the speed in which McArthur has taken to life at his new club.
"James has looked extremely natural, as though he has been playing for Wigan Athletic for a few seasons already," the Spaniard told the Wigan Observer.
"Within five minutes he was shouting for the ball, organising the team and working very hard.
"That comes natural to him.
"Physically, he is very capable and he is a great prospect. And it's only a matter of time before we see him playing for Scotland."