The moment of inertia \ensuremath{\Theta} of a trapped superfluid gas of atomic fermions ${(}^{6}\mathrm{Li})$ 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 ${T}_{c}$ 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.