Abstract. Microwave (1–300 GHz) dual-polarization measurements above 100 GHz are so far sparse, but they consistently show polarized scattering signals of ice clouds. Existing scattering databases of realistically shaped ice crystals for microwaves and submillimeter waves (>300 GHz) typically assume total random orientation, which cannot explain the polarized signals. Conceptual models show that the polarization signals are caused by oriented ice particles. Only a few works that consider oriented ice crystals exist, but they are limited to microwaves only. Assuming azimuthally randomly oriented ice particles with a fixed but arbitrary tilt angle, we produced scattering data for two particle habits (51 hexagonal plates and 18 plate aggregates), 35 frequencies between 1 and 864 GHz, and 3 temperatures (190, 230 and 270 K). In general, the scattering data of azimuthally randomly oriented particles depend on the incidence angle and two scattering angles, in contrast to total random orientation, which depends on a single angle. The additional tilt angle further increases the complexity. The simulations are based on the discrete dipole approximation in combination with a self-developed orientation averaging approach. The scattering data are publicly available from Zenodo (https://doi.org/10.5281/zenodo.3463003). This effort is also an essential part of preparing for the upcoming Ice Cloud Imager (ICI) that will perform polarized observations at 243 and 664 GHz. Using our scattering data radiative transfer simulations with two liquid hydrometeor species and four frozen hydrometeor species of polarized Global Precipitation Measurement (GPM) Microwave Imager (GMI) observations at 166 GHz were conducted. The simulations recreate the observed polarization patterns. For slightly fluttering snow and ice particles, the simulations show polarization differences up to 11 K using plate aggregates for snow, hexagonal plates for cloud ice and totally randomly oriented particles for the remaining species. Simulations using strongly fluttering hexagonal plates for snow and ice show similar polarization signals. Orientation, shape and the hydrometeor composition affect the polarization. Ignoring orientation can cause a negative bias for vertically polarized observations and a positive bias for horizontally polarized observations.