Here is my solution, it requires the lubridate package. You can use the ymd function of the lubridate package as a "replacement function". Just pick the column you want to convert ad replace it with the ymd version of it.
library(lubridate)
data[ , 1 ] <- ymd(data[, 1])
This package provides more functions to parse data or strings to dates, ymd (y = year, m = month, d= day) all with this simple scheme.