We present 3D fully kinetic shearing-box simulations of pair-plasma magnetorotational turbulence with unprecedented macro-to-microscopic scale separation. While retrieving the expected fluid behavior of the plasma at large scales, we observe a steepening of turbulent spectra at kinetic scales and substantial angular-momentum transport linked with kinetic processes. For the first time, we provide a definitive demonstration of nonthermal particle acceleration in kinetic magnetorotational turbulence agnostically of shearing-box initial conditions by means of a novel strategy exploiting synchrotron cooling.