The 20-year-old has joined the League One side until the end of the season having previously been farmed out to Inverness, Raith Rovers, Dunfermline and Hamilton.
The move reunites the youngster with Bairns boss John McGlynn, who was his manager at Raith during his six-month stint with the Kirkcaldy club during the 2020-21 campaign.
Falkirk claim to have beaten several clubs to seal a deal for the Scotland youth international, who joined his new team-mates for training on Thursday.
“Kai is a player Paul [Smith] and I have worked with previously at Raith Rovers," McGlynn said. "We enjoyed working with him and he enjoyed working with us, and we hope that will be the same again. Kai gives us real competition in the wider areas, he can play at both sides and in a number 10 position.
“He’s going to be in competition with the guys who are already in the team, and he needs to force himself in which is exactly what he’s going to try and do. It will breed good competition with others trying to play well to stay in the team.
“Kai has come here to do well, he wants to kick his career on and we’re looking to help him, and all the other players here at Falkirk with that. We’re still looking within the transfer market, and we are still hopeful that we’ll be bringing others in. I would like to thank everyone at Rangers who has made this loan deal possible.”