You need to create a valid date string by adding the year before converting it into a date type variable.
df <- data.frame(col = c("01/07", "02/07", "03/07"), stringsAsFactors = TRUE)
str(df)
#> 'data.frame': 3 obs. of 1 variable:
#> $ col: Factor w/ 3 levels "01/07","02/07",..: 1 2 3
df$col <- as.Date(paste(df$col, "2018", sep = "/"), format = "%d/%m/%Y")
df
#> col
#> 1 2018-07-01
#> 2 2018-07-02
#> 3 2018-07-03
Created on 2020-10-11 by the reprex package (v0.3.0)