The Ibrox star made his Scotland debut in the 3-0 loss to France last week.
The youngster enjoyed a fine campaign under Mark Warburton’s leadership, playing a key role in their return to the Scottish Premiership.
His displays were also rewarded in the end of season awards as he walked away with the PFA Young Player of the Year and the PFA Goal of the Season prizes.
That fine season did enough to convince the international set up, as Scotland boss Gordon Strachan named him in the squad to face Euro 2016 hosts France. He was handed his debut in that game, a disappointing 3-0 loss to Didier Deschamp's highly rated side.
Nonetheless, McKay was pleased with his performance and saying he will look to keep improving to secure more caps in future.
“You can always improve. I am sure the players we played against would say the same,” he told rangers.co.uk.
“I would love to play for my country again. To be able to make my first-team debut was a proud moment for me. I think I did okay playing against one of the best teams, if not the best team, in Europe.”
Rangers' return to the Scottish Premiership is likely to do McKay’s chances of being in the Scotland team in future the world of good.
If he can continue to impress as he did this past season, then there is every chance he can play a part when the qualifying for the next the World Cup gets underway.