The 20-year-old has been playing fly-half for Wasps with considerable success, but Jonny Wilkinson retains the England number 10 shirt.
Cipriani's two previous England appearances both came during the current RBS 6 Nations campaign as a substitute against Wales and Italy.
England head coach Brian Ashton makes two other changes from the side that beat France 24-13 in Paris 10 days ago.
Bath hooker Lee Mears is preferred to Bristol veteran Mark Regan, who misses out completely, with Leicester forward George Chuter providing bench cover.
It will be Mears' 22nd cap, but only his fourth start, and first since England faced South Africa at Twickenham in November 2006.
Ashton's decision could signal the end for 36-year-old Regan as an international player after 46 caps during a Test career that started more than 12 years ago.
Chuter, meanwhile, has not been on England Test duty since the World Cup last autumn.
The other switch is enforced, as Leicester flanker Tom Croft takes over from Wasps' James Haskell.
Haskell suffered an ankle injury during the France clash and was replaced by 6ft 5in Croft barely 20 minutes into the game.
Balshaw's demotion is no surprise, given that he has struggled for form throughout the tournament.
And Cipriani, unquestionably the hottest property in English rugby since Wilkinson, now has a chance to show what he is made of in the cauldron of a Calcutta Cup occasion.
He is no stranger to the full-back position, having featured there for Wasps before Christmas, and he should help give England a far greater attacking thrust.
England are still in the RBS 6 Nations title shake-up, but their points difference is vastly inferior to current leaders Wales.
Realistically, they need victory over Scotland - and by a sizeable margin - to remain in the hunt ahead of meeting Ireland at Twickenham on Saturday week.