U's boss Martin Ling told the club's website: "Scott is a quick ball carrier and the type of player we need since the loss of Willmott.
"He's been playing League Two football this season and due to the change in manager has become available."
Nielsen attracted the attention of league clubs in the 2008/09 season, scoring 13 goals in 46 appearances with Southern League Premier side Cambridge City.
A trial with Norwich City in the summer of 2009 was followed by a permanent move to Bradford, where he has featured 21 times.
Since the appointment of new manager Peter Taylor at Valley Parade, Nielsen has found himself out of favour.
The former Ware player is available for Cambridge's trip to Barrow this weekend.
Source: BBC Sport
Source: BBC Sport