Deadlands is pretty much set during the end of the civil war and the aftermath, now it has a lot of magic/supernatural aspects (native american shamans, magicians who make deals with the devil, steampunk mad scientists, and faith healers) and it's an alternate history game set in a wild west with magic and the civil war grinding along back east to a stalemate, but it's pretty usable for the civil war without the fantastic or alternate history aspects.
Civil War gear and "crunch" to fit d20 Modern to the era was in d20 Past, if that's your thing.
GURPS probably could do it halfway decently, but I'm no expert on that system.