There are several companies that have car rental offices. These offices are located in the Terminal building at the Arrivals end.
The companies are:
CICAR
Autoreisen
Payless
Hertz
Avis
TopCar
Sixt
Europcar
Goldcar
Just outside the airport is Pluscar.
In Caleta de Fuste there are several car rental offices:
CICAR
Avia
Autos Victor
Orlando
Hertz/Dollar/Thrifty
Ecocar
Jurecar
Best Choice
Tropic
Tip: Before booking a rental car always check out reviews, such as on TripAdvisor and make sure there are no hidden extras.