The 19-year-old has linked up with Steven Pressley’s men ahead of their League Two clash at home to Mansfield Town on Saturday, and will remain at Brunton Park until the end of the current campaign.
Denmark youth international Sørensen hit 20 goals for the Magpies’ under-23 side last term, and also spent time on loan at Blackpool in League One.
The former HB Köge forward, who joined United in the summer of 2016, made his bow for his country’s under-21s earlier this year, and has netted three times in five games at youth level for Denmark.
He featured for Steve Bruce's first team during pre-season, playing against Wolverhampton Wanderers and West Ham United in the Premier League Asia Trophy in China.
He joins a Carlisle side who currently sit 10th in the fourth tier, with two wins and a defeat from their first three games in the league and Carabao Cup.