Can I return a faucet that I bought few years back without a receipt?

No

A few years ago? I am guessing no. That would be way out of anyone's return period, receipt or no receipt.

Give it to Goodwill.

I'm not sure if you can, maybe if it was a month ago and still quite new. But after a few years I don't think so, but if it's still inside the original packaging and brand new you can try it but don't get your hopes up.