He has joined the Cumbrians on an initial one-month loan deal in a bid to play more first-team football.
Alnwick, 21, who came through the ranks at Sunderland before joining Spurs for £1million in January 2007, has previously been loaned out to Luton Town and Leicester City.
"With the change of management and the influx of foreign keepers at White Hart Lane, he has been on the fringes of their first team, but he has had some good loan spells while he has been there," manager John Ward told the club's official website.
"It's a position that we feel needs to be freshened up, so we've spoken to Tottenham and agreed to get him up here for a month."
Ward also confirmed that Alnwick will play against Peterborough United on Saturday after revealing that regular number one Ben Williams needs to 'step out' of the firing line.