Rossiter made his Rangers debut in the clash with Stranraer at Ibrox on Monday.
Rossiter is one of nine new faces at Ibrox this summer in what has been a busy transfer window for manager Mark Warburton.
He was among the first to agree a move to Scotland, but has had to wait for his debut because he has been away with the England under-19s at the European Championships.
He was handed his first appearance on Monday though, coming on as a second-half substitute in the comfortable 3-0 cup win over Stranraer.
And he says it was a great feeling to finally run out at Ibrox, saying the atmosphere was unbelievable.
“It was some feeling running out there. I signed back in May and I’ve waited a long time to make my debut,” he told rangers.co.uk.
“The atmosphere was unbelievable, it’s probably the one of the biggest crowds that I’ve played in front of and the atmosphere was great and all of the players did well.”
It now remains to be seen if Rossiter will be a regular for Rangers in the upcoming campaign.
Warburton has a number of options available to him in the middle of the park, with that area of the team arguably the most competitive.
Indeed, with Joey Barton and Niko Kranjcar both in the squad it is expected Rossiter will initially be a back up, but with the season yet to get underway places are up for grabs and he will be hoping he can stake his claim.