Several of the current and next-generation cosmic microwave background
(CMB) experiments have polarimetric capability, promising to add to
the finesse of precision cosmology. One of the contaminating Galactic
foregrounds is thermal emission by dust. Since optical interstellar
polarization is commonly seen, from differential extinction by aligned
aspherical dust particles, it is expected that thermal emission from
these grains will be polarized. Indeed, in the Galactic plane and in
dark (molecular) clouds, dust emission in the infrared and
submillimetre has been measured to be polarized. It seems likely that
the faint diffuse cirrus emission, of more relevance to CMB
experiments, will be polarized too. We discuss how well the amount of
polarization of this component can be predicted, making use of what is
known about optical (and infrared and ultraviolet) interstellar
polarization and extinction. Some constraints on the alignment of the
carrier of the dust-correlated anomalous microwave emission can be
made as well.