The 20-year-old Irish-American striker, US College Player of the Year last season, arrived this week at Murray Park for a week's training.
Lapira, capped by Republic of Ireland boss Steve Staunton last May against Ecuador as an amateur, will finish a business management degree at Notre Dame before concentrating on his football career.
"It doesn't matter too much, though, because I was always going to go back home until the end of the year to finish my studies.
"There is no point going this far and not finishing my studies. In saying that, I would like to play in Europe and it was great yesterday.
"I was maybe going to go to Aberdeen, but I am delighted to come to Rangers and see what happens. I have an EU passport through dual nationality, so I might as well use that to get me into European football."
Gers boss Walter Smith says Lapira has come here highly recommended, and it's likely an arrangement will be made for him to return early in the New Year.
Smith said: "The lad picked up an injury yesterday, and there will be no quick decision. You have to remember he is still an amateur, but we would like to have a longer look at him."