The 24-year-old winger, who became a free agent in December, has spent the last four years at Major League Soccer side Columbus Crew.
Simon Grayson told the club's official website: "We're delighted to have agreed a deal with Robbie. He's been training with us and came to Arsenal to get a feel of the group.
"He has been playing in the MLS where he's done well, he wants to continue his career in Europe and we believe he'll make an impact here.
"As soon the work permit business is complete he will be an immediate part of our plans and have an opportunity with the first team."
Californian Rogers spent one season with Dutch side Heerenveen in 2006/07, but never made the first team and returned to America with Columbus Crew the following year.
Source: FOOTYMAD
