Buongiorno,
It is a possibility to get a private taxi service (just do a search for NCC Florence in Google) from the airport. However the airport is small, not that much traffic and there are taxis available when you get out of the gate. You will most probably need two because there aren't normally a lot of the larger ones always available.
The distance is not so very far, that personally I would just take the taxi which is available to the historic center.
Buon Viaggio