Can transverse sound waves be polarized?

These transverse waves are known as S-waves or shear waves and yes they can be polarized. Waves that are polarized in the horizontal direction are known as SH-waves and those in the vertical direction are known as SV-waves. These waves exhibit the property that when they meet a boundary between two mediums (say solid -> air) they can turn into P-waves, which are the more well know compression waves.

When they are polarized as SH-waves it means that the particle motion in the solid is contained in the horizontal plane, and the same goes for SV-waves except in the vertical plane.

"Sound" is a pressure phenomenon, and has no polarization.

It is possible to send acoustic shear waves through an elastic solid (and that transverse component can have a direction) - but not through a gas.

Just to confuse you more - in an anisotropic medium, different directions of shear may propagate at different velocities, resulting in an apparent rotation of the direction over time (and in fact it can go from linear to circular polarization, etc).