The 22-year-old comes in to the squad as cover on the right side of Penney's backline following a successful trial and reserve appearance last week.
It ends Mulligan's search for a new club since his release from a weekly contract with Division Two side Barnsley back in October.
After an unsuccessful trial at Sheffield United, Mulligan decided to try his luck with Donny and he has impressed enough to earn a deal with the Division Three high-flyers.
The New Zealander was delighted to sign a short-term deal with the club and hopes it will lead to a successful spell at Belle Vue.
"I knew from my mate Ricky Ravenhill, who was at Barnsley with me, that this was a good club with great facilities and a great set of lads," Mulligan told the club's official website.
"I hope I can show at Scunthorpe for the reserves that I can do a job for this club and make my full debut in the big game at Mansfield."
One player who will not be joining the club is veteran midfielder Neil Redfearn.
The 38-year-old, who is currently at Division Three rivals Boston United, was reported to be on the verge of putting pen-to-paper with Donny after allegedly leaving The Pilgrims following the sacking of manager Neil Thompson last week.
However, Penney has stated that there is no truth to the report.
"There is no truth in this and we have no knowledge of it," said Penney.
