Create new variable order based on "year"

Dear everybody,
I would like to ask for help. I would like to create a new variable named "order", which based on the order of the year. (For example , 2001 -> 1; 2002 ->2, 2003->3 )
I would like to ask for help. Thank you in advance.

data.frame(
        year = c(2001L,2002L,2003L,2004L,2001L,2002L,
                 2003L,2004L,2001L,2002L),
      ticker = as.factor(c("AAA","AAA","AAA",
                           "AAA","BBC","BBC","BBC","BBC","DCC","DCC"))
)

Take a look at ?rank

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