This model Rolex has been manufactured over multiple years, and it is not possible to date your watch based purely on is model number. However, it is possible to date most Rolexes based on their serial numbers, which can be found stamped between the lower lugs (i.e., the lugs below 6:00 on the watch dial). You will need to remove the band from these lugs to read the serial number.
Dating the watch case of a Rolex does not necessarily date the entire watch. It is possible that a movement from another watch was placed into a watch case that is younger or older than the the movement. Like Rolex watch cases, Rolex movements can also be dated by their serial numbers, if this is a concern you have about this particular watch.
This jeweler has put together a nice summary of when Rolex watch models were introduced and which serial numbers are associated with specific years of manufacture. Once you have found your serial number, this should help you date your watch. I have no connection (financial or otherwise) with this web site, but I found the information useful and presented in an easy to understand way.