Did Shelob know about the Ring? Considering she doesn't really have fingers, could she have used it if she had known about it?
She didn't know or care about it.
Little she knew of or cared for towers, or rings, or anything devised by mind or hand, who only desired death for all others, mind and body, and for herself a glut of life, alone, swollen till the mountains could no longer hold her up and the darkness could not contain her.
-- The Two Towers, chapter "Shelob's Lair"
This is consistent with what we know about her character. She shows intelligence only in a brutish, beastly sort of way. Her existence revolves around luring creatures into her traps and devouring them; a Ring of Power would have little interest to her. She wouldn't have used it even if she knew about it.
That doesn't, of course, account for the effect the Ring has on everyone (except Tom Bombadil) who comes into contact with it. Perhaps even a creature usually unmotivated by powerlust would be affected by the addiction of the Ring. But:
- Given that Gollum would come to take it almost immediately after she first came into contact with it, the Ring wouldn't have much time to take hold of her. Her lack of care for such things would probably take time to wear down, especially given her immense age, and the Ring wouldn't be able to do that in the short time that she would 'possess' it before Gollum seized it back.
- She's not the sort of creature the Ring would want to possess anyway. With Gollum it was content to spend centuries hiding in a mountain, while its master was also in hiding. But now that Sauron is trying to take over the world again, the cracks of Shelob's lair aren't where the Ring really wants to be.
Disclaimer: I mostly copied this from my own answer to a similar question at Literature SE.