This article describes one of the scattering algorithms of the three-dimensional polarized radiative transfer model ARTS (Atmospheric Radiative Transfer Simulator) which has been implemented to study for example the influence of cirrus clouds on microwave limb sounding. The model uses the DOIT (Discrete Ordinate Iterative) method to solve the vector radiative transfer equation. The implementation of a discrete ordinate method is challenging due to the spherical geometry of the model atmosphere which is required for the simulation of limb radiances. The involved numerical issues, which are grid optimization and interpolation methods, are discussed in this paper. Scattering simulations are presented for limb- and down-looking geometries, for one-dimensional and three-dimensional spherical atmospheres. They show the impact of cloud particle size, shape, and orientation on the brightness temperatures and on the polarization of microwave radiation in the atmosphere. The cloud effect is much larger for limb radiances than for nadir radiances. Particle size is a very important parameter in all simulations. The polarization signal is negligible for simulations with completely randomly oriented particles, whereas for horizontally aligned particles with random azimuthal orientation the polarization signal is significant. Moreover, the effect of particle shape is only relevant for oriented cloud particles. The simulations show that it is essential to use a three-dimensional scattering model for inhomogeneous cloud layers. ; This article describes one of the scattering algorithms of the three-dimensional polarized radiative transfer model ARTS (Atmospheric Radiative Transfer Simulator) which has been implemented to study for example the influence of cirrus clouds on microwave limb sounding. The model uses the DOIT (Discrete Ordinate Iterative) method to solve the vector radiative transfer equation. The implementation of a discrete ordinate method is challenging due to the spherical geometry of the model atmosphere which is required for the simulation of limb radiances. The involved numerical issues, which are grid optimization and interpolation methods, are discussed in this paper. Scattering simulations are presented for limb- and down-looking geometries, for one-dimensional and three-dimensional spherical atmospheres. They show the impact of cloud particle size, shape, and orientation on the brightness temperatures and on the polarization of microwave radiation in the atmosphere. The cloud effect is much larger for limb radiances than for nadir radiances. Particle size is a very important parameter in all simulations. The polarization signal is negligible for simulations with completely randomly oriented particles, whereas for horizontally aligned particles with random azimuthal orientation the polarization signal is significant. Moreover, the effect of particle shape is only relevant for oriented cloud particles. The simulations show that it is essential to use a three-dimensional scattering model for inhomogeneous cloud layers.