For the purpose of illustration let's assume the Ringworld has a radius of 1AU and is as broad as earth is wide, so around 12000km. There are two differen aspects to your question: How does the curvature of the Ring look like from it's surface and how bright is it.
Assuming an Earth-like surface we can assume around the same absolute magnitude for a roughly earth-sized segment as for earth. Given that we can see Venus just fine and it is one of the brightest objects in the night sky the ring, which is much bigger should be quite obvious in the night sky (I'm assuming a Niven-style day/night system here where an inner ring with partial segments rotates to block the sun for night time over a part of the Ringworld). You would see a segmented line go right over your head. I don't expect you to see anything during the day though since you can't see Venus either when the sun is up an noon, and on a Ringworld it's always noon or solar eclipse night.
As for the curvature near the horizon that's more tricky. With geometry (Thales' theorem is useful here) it's clear that distance of two points on a circle is Diameter times sin(x) where x is the angle between the circle tangent at one point and the secant connecting the two points. So if you're looking at a part of the ringworld the angle x is what you have to look up from your local horizontal.
You can see stars even just a couple of degrees over the horizon so we can go deep. At 2° you are looking 35 light seconds away. Earth in that distance would have an angular diameter of about four arc minutes. That's not big, about one sixth of the full moon. So you could see that it has a diameter and probably even some structure if you have good eyes or a primitive telescope. But it's not the big "circle curves in to become your horizon" a lot of ring world illustrations show.
Tl,dr: In the dark it should be a bright line going over the sky. But the curvature and nature as a circle only becomes visible at low angles so you could easily imagine people living in regions with hills and low visibility and you could miss the circle nature of the world from there. At an ocean with good conditions it should be obvious though.