The 22-year-old attacking midfielder, who has scored 64 goals in two years for Northern League side Penrith, was handed a trial by boss Graham Kavanagh in the summer.
And Rigg has done enough to persuade the Cumbrians to hand him a professional contract, scoring in a 5-1 win over Southampton under-21s and playing 90 minutes against Penrith on Tuesday evening as part of the League Two club's pre-season commitments.
"Steven has obviously been playing at Penrith, which is a lower level than us, but with the amount of goals he scored last season we had to have a look at him," Kavanagh told Carlisle's official website.
"He's a goalscorer and he knows where the net is, but there are areas of his game we want him to work on. He's never been a professional player before and he hasn't worked in the game full time, so it will be interesting to see what sort of fitness levels he can get to.
"We want to try and improve him technically in terms of his close control and his awareness.
"It's a great opportunity for him to become a professional footballer and make his way in the game. We had a discussion as a staff the other day and, although he probably isn't quite there yet overall, he's definitely there in terms of his goalscoring.
"He's playing in what is probably our strongest area of the pitch so he will have a challenge on his hands to get into the team. That being said, it's a really good opportunity for him and I hope he takes it with both hands.
"He's done well in the games he's played so far. He's scored a couple of goals and he's been scoring in training every day. We've taken a chance on him and we'll see where it takes us."