Rouamba was a regular for his country in their surprise run to this year's African Nations Cup final where the Stallions beat Togo and Ghana before losing to Nigeria.
The defensive midfielder has spent the last six years in Moldova playing for FC Sheriff Tiraspol, who have won 11 of the last 12 league titles, including six league and cup doubles.
Rouamba played for Tiraspol in this season's Europa League where they lost to Marseille in the play-off stage.
"He has been playing out in Moldova, which is quite a strange route, but it happens with a lot of players as they just want to play, regardless of the country," Charlton manager Chris Powell told the south London club's website.
"He trained with us before the international break and we quite liked what we saw, so we've managed to secure him, hopefully, if everything is resolved with his work permit.
"He will be with us until the end of the season, which gives us a longer look at him.
"He played in the African Cup of Nations final and there has been a bit of interest in him, but it is something we can do because it is a good chance for us to look at him.
"I don't think he is used to the weather - that is one thing that has counted against us ... I think he is wondering about the snow at the moment.
"He doesn't know anyone really and he is in a hotel, and you have to take those things into account, but he is here to impress us for the longer term and I really hope that he does well and is one that can maybe add to us in the future."
Charlton are 15th in the Championship, just five points above the relegation zone.
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- FC Sheriff Tiraspol