San Francisco announced the claim on Monday.
The 6 foot 1, 294 pound defender entered the NFL as a fourth round pick by the Jacksonville Jaguars in the 2016 NFL Draft.
Day, 23, had 11 tackles, two sacks and a pass defensed in 22 games in the last two seasons. This season Day had three tackles, a sack and a pass defensed in six games for the Jaguars. He was released on Nov. 18.
San Francisco defensive coordinator Robert Saleh was the Jaguars' linebackers coach in 2016.
The 49ers have Earl Mitchell, DeForest Buckner, Tony McDaniel and D.J. Jones listed at defensive tackle on the depth chart.
The 49ers ended their nine-game losing streak to start the season in Week 10 against the New York Giants. San Francisco had a Week 11 bye and ranks No. 27 in yards allowed per game this season. The 49ers have also allowed the most scrimmage plays in the NFL at 697.