Armer takes over from Julian Danby to become the team's third skipper this season after they started the year with Marcus Steed in charge.
"I've wanted to do this for a long time and I'm really looking forward to it," said Armer.
"I think we ha
ve a lot of talent in the side and it's my job to get the best out of them and get us as high a finish as possible."
Club chairman Alan Smith added: "With this appointment, we are looking to the future.
"The intention is to groom Brad as a captain for the rest of this season and hopefully many seasons beyond.
"Julian was only ever doing the job on a temporary basis and, with him being from New Zealand, it was not certain whether he would be back with us next year or not.
"Consequently, with eight games to go and with us in mid-table, we felt it would be better to put Brad into the role now to see how he gets on with it.
"Hopefully, he will take to it well and want to continue in the role next year.
"He's been with us since he was a boy and he's certainly keen to take on the job so it made good sense to let him take it."
Armer will aim for his first win when Rushton go to Old Northamptonians tomorrow with Dave Wonfor and Tom Barker coming into the side in place of Jamie Smith and Martin Roberts.
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