Analytical expressions of the particle number density, chemical potential, total energy, specific heat and the spatial distribution of particle current density for rotating interacting Fermi gases in a harmonic trap are derived based on the local density approximation (LDA). The effect of mutual interaction between the nearby atoms plays an important impact on the thermodynamics. Especially, the spatial distribution of current density is discussed in detail. The results show that the centrifugal force caused by rotation is always competing with the binding force confined by the harmonic trap. The harmonic trap and attractive interaction tend to concentrate the particles around the center of the trap. The rotationand repulsive interaction tend to decentralize the particles away from the center, which decreases the particle number density and particle current density. Their mutual competition results in the particle distribution being more scattered. Moreover, twosharp and opposite oscillations appear in the spatial distribution of fermion current density. The numerical results indicate that the amplitude and period of oscillations in the spatial distribution of fermion current density are strongly affected by the quantum states near the Fermi surface, which play a dominant contribution to these oscillations．Compared with the case of the ideal Fermi system, the repulsive interaction increases the chemical potential and total energy while the attractive interaction decreases them. The influence of mutual interaction on the specific heat shows completely different characteristics at various temperatures. At the low temperature, repulsive (attractive) interaction makes the heat capacity larger (smaller). At the high temperature, repulsive (attractive) interaction makes the heat capacity smaller (larger) and finally tends to a constant. The results given in this paper can be treated as the general reference for the multiscale analysis of rotating ideal Fermi gases and the other Fermi system. When the mutual interaction disappears, these results completely coincide with those cases for rotating ideal Fermi gases a harmonic trap.