We have performed hydrodynamic simulations of relativistic rotational supernova core collapse in axisymmetry and have computed the gravitational radiation emitted by such an event. The Einstein equations are formulated using the conformally flat metric approximation, and the corresponding hydrodynamic equations are written as a first-order flux-conservative hyperbolic system. Details of the methodology and of the numerical code have been given in an accompanying paper. We have simulated the evolution of 26 models in both Newtonian and relativistic gravity. The initial configurations are di erentially rotating relativistic 4=3-polytropes in equilibrium which have a central density of 10^10 g cm^−3. Collapse is initiated by decreasing the adiabatic index to some prescribed fixed value. The equation of state consists of a polytropic and a thermal part for a more realistic treatment of shock waves. Any microphysics like electron capture and neutrino transport is neglected. Our simulations show that the three di erent types of rotational supernova core collapse and gravitational waveforms identified in previous Newtonian simulations (regular collapse, multiple bounce collapse, and rapid collapse) are also present in relativistic gravity. However, rotational core collapse with multiple bounces is only possible in a much narrower parameter range in relativistic gravity. The relativistic models cover almost the same range of gravitational wave amplitudes (4x10^−21 <= h^TT 3x10^−20 for a source at a distance of 10 kpc) and frequencies (60 Hz <= ν <= 1000 Hz) as the corresponding Newtonian ones. Averaged over all models, the total energy radiated in the form of gravitational waves is 8.2 10^−8 Moc^2 in the relativistic case, and 3.6 10^−8 Moc^2 in the Newtonian case. For all collapse models that are of the same type in both Newtonian and relativistic gravity, the gravitational wave signal is of lower amplitude. If the collapse type changes, either weaker or stronger signals are found in the relativistic case. For a given model, relativistic gravity can cause a large increase of the characteristic signal frequency of up to a factor of five, which may have important consequences for the signal detection. Our study implies that the prospects for detection of gravitational wave signals from axisymmetric supernova rotational core collapse do not improve when taking into account relativistic gravity. The gravitational wave signals obtained in our study are within the sensitivity range of the first generation laser interferometer detectors if the source is located within the Local Group. An online catalogue containing the gravitational wave signal amplitudes and spectra of all our models is available at the URL http://www.mpa-garching.mpg.de/Hydro/hydro.html.