Could be a bad belt tensioner, bad pulley bearing in one of the accessories (power steering pump, alternator, A?C compressor), or bad bearing in the idler pulley. When you turn the wheel, you are causing the power steering pump to load the serpentine belt slightly, that might be enough drag to change how the other pulleys are loaded.
Could also be glazed pulleys. Try spraying the belt with plain water (might add a drop or two of dishwashing soap to act as a dispersant (helps the water stick to the belt). Run the car - if the noise is gone, then you have either a faulty belt or one or more of the pulleys has some type of contaminant on the contact surface.
Dirty, contaminated fluid is another possibility. Just like other fluids, the power steering fluid needs to be replaced at regular intervals. Failure to do so will likely shorten the life of the steering pump, as contaminants will eat away at seals and facilitate corrosion.