The moment of inertia \ensuremath{\Theta} of a trapped superfluid gas of atomic fermions
(6Li) is calculated as a function of the temperature. At zero temperature the moment of inertia takes on the irrotational-flow value. Only for T very close to
Tc is rigid rotation attained. It is proposed that future measurements of the rotational energy will unambiguously reveal whether the system is in a superfluid state or not.