The 19-year-old has won eight caps for Northern Ireland, but his club career consisted solely of a six-game loan spell at Morecambe last season until he contributed to Tuesday's win over Crystal Palace.
Manager Nigel Pearson sprung a surprise by replacing regular full-backs Bruno Berner and Michael Morrison with McGivern and Robbie Neilson.
And McGivern told the club website: "Every player gets frustrated when they are not in the team, but you just have to get your head down and make sure you take the chance when it comes.
"It was the same at Manchester City. I was hanging around the squad while playing for Northern Ireland, but I have got a game under my belt and hopefully I can stay in the team."