The first mention of rubbing a wine glass rim with a moist finger is apparently by Francis Bacon (1561—1626) in his Sylva Sylvarum (1627):
9. Take a glass, and put water into it, and wet your finger; and draw it round about the lip of the glass, pressing it somewhat hard; and after you have drawn it some few times about, it will make a the water frisk and sprinkle up in fine dew. This instance doth excellently demonstrate the force of compression in a solid body: for whensoever a solid body, as wood, stone, metal, &c. is pressed, there is an inward tumult in the parts thereof seeking to deliver themselves from the compression: and this is the cause of all violent motion.... 1
Curiously, Bacon doesn't mention the sound of it (although a few paragraphs later he talks about sound in general). I've tried getting the water to 'frisk' in glasses that don't sing, and it looks like singing and 'frisking' are mutually dependent. Which is expected from the understanding of physics that we now have—the glass is going to have to be resonating (singing) for the walls of the glass to be able to put enough energy into the water to make it 'frisk'. (Try it! It won't 'frisk' until it 'sings'.)
It is very curious that he doesn't mention the sound itself—did he have a hearing problem?