First, you're talking about the hex representation, not the RGB. The RGB representation is three numbers (either between 0 and 1 or 0 and 255) giving the red, green, and blue levels.

To get the RGB representation, you can just use the base function col2rgb():

col2rgb('mediumorchid2')
#       [,1]
# red    209
# green   95
# blue   238

I have long had a personal convenience function for getting the hex representation, as it's a task I need to do often:

col2hex <- function(x, alpha = "ff") {
    RGB <- col2rgb(x)
    return(apply(RGB, 2, function(C) {
        paste(c("#", sprintf("%02x", C), alpha), collapse = "")
    }))
}
col2hex('mediumorchid2')
# [1] "#d15feeff"

Update:

Gordon Shumway's excellent answer mentions that apparently there is a package with such a function already! I would recommend that. However, I leave my answer up both for the discussion of RGB vs. hex and in case you don't want a dependency on gplot.