Based mostly on stellar models which do not include rotation, CO white dwarfs which accrete helium at rates of about $sim 10^{-8}~mathrm{M}_odot/mathrm{yr}$ have been put forward as candidate progenitors for a number of transient astrophysical phenomena, including supernovae of Type Ia, and the peculiar and fainter Type Iax supernovae. Here we study the impact of accretion-induced spin-up including the subsequent magnetic field generation, angular momentum transport, and viscous heating on the white dwarf evolution up to the point of helium ignition. We resolve the structure of the helium accreting white dwarf models with a one dimensional Langrangian hydrodynamic code, modified to include rotational and magnetic effects. We find magnetic angular momentum transport, which leads to quasi solid-body rotation, profoundly impacts the evolution of the white dwarf models. Our rotating lower mass ($0.54$ and $0.82~mathrm{M}_odot$) models accrete up to 50% more mass up to ignition compared to the non-rotating case and the opposite for our more massive models. Furthermore, we find that rotation leads to up to 10-times smaller helium ignition densities, except for the lowest adopted initial white dwarf mass. Ignition densities of order $10^6,mathrm{g/cm}^3$ are only found for the lowest accretion rates and for large amounts of accreted helium $gtrsim 0.4,mathrm{M}_odot$. However, correspondingly massive donor stars would transfer mass at much higher rates. We expect explosive He-shell burning to mostly occur as deflagrations and at $dot{M}>2cdot10^{-8}~mathrm{M}_odot/mathrm{yr}$, regardless of white dwarf mass. Our results imply that helium accretion onto CO white dwarfs at the considered rates is unlikely to lead to explosions of the CO core or to classical Type,Ia supernovae, but may instead produce events like faint and fast hydrogen-free supernovae.
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