My issue is I am planning to buy a wort chiller but my sink faucet isn't able to have anything screwed onto it. Is there some kind of adapter that can do this?
You can always rig up something non threaded including vinyl tubing and a worm-style hose clamp. Depends on your exact faucet, but it doesn't need to be pressure rated, really. If you take a pic, might help us to find you the best solution.