Yes...IF you are staying at a DVC resort on your rental. If you are staying at a non DVC resort on points, you cannot participate in the dining plan through either DVC or the Disney resort.
The member you are renting from must call Member Services and add the dining plan to your resort reservation. It cannot be added at check-in. You must pay for the plan at check-in. If you are purchasing the dining plan through DVC, there is no requirement to purchase park tickets.