%m/%Y
is a tricky starting format for a date, if that's what you ultimately need:
grab date components from the string:
aa <- format(Sys.Date(), "%m/%Y")
m <- as.numeric(substr(aa, 1, 2))
y <- as.numeric(substr(aa, 4, 8))
Then you can paste them together into a date format and sort:
as.Date(paste(y, "-", m, "-01", sep = ''))