Turbulence in the Earth's magnetosheath at ion kinetic scales is investigated with the magnetospheric multiscale spacecraft. Several possibilities in the wave paradigm have been invoked to explain plasma turbulence at ion kinetic scales such as kinetic Alfvén, slow, or magnetosonic waves. To differentiate between these different plasma waves is a challenging task, especially since some waves, in particular, kinetic slow waves and kinetic Alfvén waves, share some properties making the possibility to distinguishing between them very difficult. Using the excellent time resolution data set provided from both the fluxgate magnetometer and the Fast Plasma Instrument, the ratio of trace velocity fluctuations to the magnetic fluctuations (in Alfvén units), which is termed the Alfvén ratio, can be calculated down to ion kinetic scales. Comparison of the measured Alfvén ratio is performed with respect to the expectation from two-fluid magnetohydrodynamic theory for the kinetic slow wave and kinetic Alfvén wave. Moreover, the plasma data also allow normalized fluctuation amplitudes of density and magnetic field to be compared differentiating between magnetosonic-like and kinetic Alfvén-like turbulence. Using these two different ratios, we can rule out that the fluctuations at ion scales are dominated by magnetosonic-like fluctuations or kinetic slow-like fluctuations and show that they are consistent with kinetic Alfvén-like fluctuations. This suggests that in the wave paradigm, heating in the direction of the parallel magnetic field is predominantly by the Landau damping of the kinetic Alfvén wave.