Empty the bowl and using a sponge, and rubber gloves, to remove the water from the trap-way.
If the ring is rough and uneven to the touch, it's a indication of calcium deposits.

The acid will cause nasal discomfort so keep the area ventilated.

Pour some muratic acid into the bottom of the bowl and using some brown Scotch-Brite, moistened with the acid, gently scrub the ring.

The treatment may not cure the problem entirely, and I would caution against using a stronger acid, that you are not familiar with.

Then you might consider running soft cold water to the bathroom - esp if you have other old fixtures. I did that to protect my old claw tub - no lime deposits to scrub off is well worth the cost! Once the porcelain gets worn the deposits seem to stick on more and be harder to get off.

I would try using fine grit sandpaper ...

Try a Pumice stone. Also a cleaner called "Barkeepers Friend"

Diane

Vinegar dissolves hard water lime.

I'd try vinegar first. Stronger cleaners can etch the porcelain creating a rough surface that is permanently damaged. I know because I etched my tub by using a strong cleaner, don't remember which one, maybe CLR. I could kick myself, especially after the plumber had already warned me to be gentle with the cleansers on the old bathroom fixtures.

I've had good luck with the sponge-like Mr. Eraser by 3M, I think.

First try an abrasive cleaner called Zud. Acid by itself may remove the surface glazing so it should be the last resort.

Here is a link that might be useful: Zud

Before you opt for more abrasive things and possibly scratch the surface, do try Barkeepers Friend. Apply and let it sit for awhile, then scrub with a plastic scrubbie. I tried multiple things on an old toilet ring and was amazed when this worked. It really is wonderful stuff, with multiple uses. It can be found in most grocery stores, with the cleansers.

BKF and Zud are both abrasive cleansers with oxalic acid but Zud has more of it and uses pumice and finely ground quartz for tougher jobs. So you could try BKF first but I would start with Zud and increase the exposure and pressure gradually. I've never known it to damage porcelain but I guess that's possible.

I have however destroyed the surface of a porcelain tub with diluted acid drain cleaner (essentially muriatic acid) that drained back into the tub for just a few minutes.