We analyze resonant inelastic x-ray scattering (RIXS) at the Cu K edge in a typical orbital-ordered compound KCuF3 on the basis of a microscopic theory. Spectral shape and its dependence on polarization direction and momentum transfer of photons are explained consistently with experimental data within our microscopic calculation. According to our microscopic orbital-resolving analysis, high-energy spectral weights (above 5 eV) originate from charge-transfer excitations related to the Cu-d\gamma orbitals, while the low-energy weights (below 2 eV) originate from the d-d orbital excitations among the five Cu-d orbitals. We assign specifically the RIXS weights to microscopic orbital-excitation processes, beyond the previous phenomenological assignment based on symmetry properties.