Anderson had been available for transfer at Griffin Park and had a loan spell at Wycombe Wanderers earlier in the campaign.
The 27-year-old had spent almost a fortnight on trial with Rovers and impressed Pirates manager Ray Graydon in two reserve team outings.
Graydon was happy with his new recruit and is confident the full back can slot easily into his system.
"I am delighted to have Ijah on board," Graydon told the club's official website.
"We have a major problem with the left back position, and with Trevor Challis needing an operation and likely to be out for some time yet, Ijah can come in and slot straight into the 4-4-2 formation.
"He is aggressive, quick and likes to get forward, and he has impressed us in the couple of reserve games he has played in for us."
Anderson made his Rovers debut in Saturday's 2-2 draw against former club Southend United.
