Access has an import funtion to do what you wish.
File/Get External Data/Import. Change the search file extension to *.dbf (choose dBaseIII from the drop down menu). I don't have a dBaseIII file to test on at the moment, but seems like I've been successful at this in the past. (btw, I'm looking at MS Access'97, so on newer versions, the Import utility might be in a different menu location.)
hth
dennis