Sound waves (through compressible media) cause temporary compression of the medium through which they travel. This compression temporarily raises the temperature. If the sound waves are intense enough, the temperature may rise to the point that the medium emits light. It is called sonoluminescence.
Since you edited your question to ask about ionized air, and not just air in general, I feel that is an important point to be made.
Yes, sound waves through ionized air will cause the motion of charges. This motion of charges will produce electromagnetic waves. Although light is an electromagnetic wave, the frequency of light waves is far to high to be produced by the oscillation of ions by sound. What will be produced by such oscillations is radio waves.
[It may take this question too far afield, but the radio waves produced in such a manner will be quite weak. Because light waves are "short", they do not need to be "coherent" to be easily detected. Light waves, thus exhibit a kind of "particle" behavior. (Think photons). Radio waves generated close together, however, will interfere with one another if they are not "coherent". Ionized air, (or plasma) generally contains both positive and negative charges. The sound waves through the ionized air will cause both the positive and negative charges to move. It seems likely that much or most of the oscillating electromagnetic fields generated by these sound-driven moving charged particles will cancel, and the resultant radio waves generated by them will be weak. These resultant waves may perhaps be too weak to be distinguished from background radio-frequency noise.]