The simultaneous emergence of active turbulence and odd viscosity for a colloidal rotors system is here shown. Rod-like colloidal particles with a ferromagnetic head and magnetic moment perpendicular to the rod axis, precess vertically to the substrate under an externally rotating field. The colloid rotation drags the adjacent fluid inducing the translation of neighbouring colloids, behaviour which is also captured by hydrodynamic simulations of discs rotating in sync. Experiments and simulations reveal that multi-scale eddies emerge with an energy spectrum following a power-law decay: this feature of self-similar dynamics without the emergence of a dominant vortex size is characteristic of active turbulence. Moreover, the particles are dragged to the center of the vortices, a telltale sign of systems with odd viscosity, which is explicitly measured. Our findings are relevant for the understanding of biological systems and for the design of microrobots with collective self-organized behavior.