Oscillation modes of a mixed character are able to probe the inner region of evolved low-mass stars and offer access to a range of information, in particular, the mean core rotation. Ensemble asteroseismology observations are then able to provide clear views on the transfer of angular momentum when stars evolve as red giants. Previous catalogs of core rotation rates in evolved low-mass stars have focussed on hydrogen-shell burning stars. Our aim is to complete the compilation of rotation measurements toward more evolved stages, with a detailed analysis of the mean core rotation in core-helium burning giants. The asymptotic expansion for dipole mixed modes allows us to fit oscillation spectra of red clump stars and derive their core rotation rates. We used a range of prior seismic analyses, complete with new data, to get statistically significant results. We measured the mean core rotation rates for more than 1500 red clump stars. We find that the evolution of the core rotation rate in core-helium-burning stars scales with the inverse square of the stellar radius, with a small dependence on mass. Assuming the conservation of the global angular momentum, a simple model allows us to infer that the mean core rotation and envelope rotation are necessarily coupled. The coupling mechanism ensures that the differential rotation in core-helium-burning red giants is locked.