Rovers are keen for more options in the centre of defence to provide alternatives to 40-year-old Ian Goodison and Ash Taylor and only last Saturday they brought in Huddersfield full-back Liam Ridehalgh on a three-month deal.
McNulty, 28, can play at either centre-back or at left-back, which is another position of concern for Tranmere given Danny Holmes' illness and Evan Horwood's groin injury.
Moore told Rovers' official website: "With Adam Dugdale returning to Crewe we are low on numbers in defence so I'm delighted to have signed Jim for a month.
"We've got a lot of young players on the pitch at the moment so Jim's experience will be useful.
"He's a player I've been keen on for a while. He can play in a couple of positions, is big and strong and uses the ball well."