Not that I know of on sight, but there are a bunch at the airport which is about 1 mile away. You could try calling any of the companies, Budget, Dollar, Avis, Hertz, etc., and see if they would have a shuttle to pick you up at the port. Otherwise, the cab fare is around $10 to the airport. Best wishes!!
We have reserved cars at National and Alamo in the past in Fort Lauderdale. They offer free pick-up at Port Everglades and do not need to be called in advance.
We most recently rented a car with National. Their free shuttle can pick you up at Port Everglades and then they take you to their location near the airport. I don't know if they will provide transportation back to PE. I guess it might be worth a phone call. We've done business with them several times and the next time we are in that area, we will again.