  Context. Planck observations demonstrated that the grain alignment efficiency
is almost constant in the diffuse ISM. Aims. We test if the Radiative Torque
(RAT) theory is compatible with observational constraints on grain alignment.
Methods. We combine a numerical simulation with the radiative transfer code
POLARIS that incorporates a physical dust model and the detailed grain
alignment physics of RATs. A dust model is designed to reproduce the spectral
dependence of extinction of the ISM. From a RAMSES simulation of interstellar
turbulence, we extract a cube representative of the diffuse ISM. We
post-process the cube with POLARIS to get the grain temperature and RATs to
simulate synthetic dust polarization maps. Results. In our simulation the grain
alignment efficiency is correlated with gas pressure, but not with the RAT
intensity. Because of the low dust extinction, the magnitude of RATs varies
little, decreasing only for high column densities $N_H$. Comparing our maps
with a uniform alignment efficiency, we find no systematic difference. The
dependence of polarization fraction $p$ with $N_H$ or polarization dispersion
$S$ is similar. The drop of RATs in dense regions barely affects the
polarization pattern, the signal being dominated by the LOS and magnetic field
geometry. If a star is inserted, the polarization increases, with no specific
pattern around the star. The angle-dependence of RATs is not observed in the
maps, and is weak using a uniform magnetic field. Conclusions. RATs are
compatible with Planck data for the diffuse ISM such that both uniform
alignment and RAT alignment lead to similar observations. To further test the
predictions of RATs where an important drop of grain alignment is expected,
polarization observations of dense regions must be confronted to numerical
simulations sampling high column densities through dense clouds, with enough
statistics.
