Richardson made 20 appearances for the Millers last term, but has been without a club since being released in May.
The 33-year-old started his career at Leeds United and has also had spells with Stoke, Charlton, Southampton, Middlesbrough and Ipswich.
"I haven't had too much football but I've been keeping myself right so I'm good to go," he said.
"There's a really good set up here, a great bunch of lads and Darren Ferguson and his backroom staff are a good management team."
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Former Rotherham defender Frazer Richardson has joined League Two side Doncaster Rovers on a two-month deal.