The Gas won five of their seven games in what was a busy period with the first three weeks having midweek and weekend fixtures.
They only dropped points to a resurgent Carlisle United and to their promotion rivals Newport County, both away from home.
Rovers recorded four clean sheets in their five victories and conceded just five goals in the process.
“I’m delighted to win manager of the month,” said Barton.
"It’s a collective win for our group and a testament to the hard work put in by staff and players. The players, in particular, have continued to improve and as we enter the championship rounds, we must capitalise on our momentum and continue to turn up and pay our dues every day if we are to get what we want from this season.”
He saw off the challenge from the likes of former Bristol City coach Paul Simpson, Salford City’s Gary Bowyer and Matt Taylor of Exeter City.
Former Sheffield United, Wednesday and Barnsley boss Danny Wilson, was part of the panel which was deemed the winner.
“Joey Barton’s men had a super return of points to continue a very impressive consistent run of form,” said the 62-year-old who has overseen more than a 1000 games in management.
“15 points came from their seven games, only conceding three goals, gives them a deserved place in the play-off positions in March.”
As well as an award for Barton, Elliot Anderson has been nominated for the Goal of the Month, for his dazzling solo goal against Harrogate Town.
The on-loan Newcastle United midfielder picked the ball up on the flank and danced through four defenders before coolly slotting past the goalkeeper.
The vote is open to fans and Rovers supporters have three days to ensure that the club have a double award for March.
Leyton Orient’s Ruel Sotiriou won the Player award as he scored six goals in eight matches, which helped Richie Wellens’ side to safety.