Assuming that this ring is visible, it would most certainly need to go into star charts. However, how that ring goes around the earth is important. Is it a simple ring, which hovers around our equator? Are there any complicated behaviors of the ring, such as precession or "wobbling"?
Simple Ring System
If ring forms along the equator, then you get to see star charts like the on you've pictured with a boarder. This is no big deal- you just see the equator marked with the "ring."
If the ring is off-kilter, that is, it's at an angle relative to the equator, this would look different on star charts. It depends on the angle, but it can form a swirl. It'll look like the milky way on your star chart- an "s" shaped curve. The curve goes from super-curvy when the ring is very close, but not quite in line with the equator, to very flat, when it's 90 deg. on the star chart.
This assumes the ring, if it is tilted, rotates with the earth so that the places under the ring are always under the ring. (That is, the individual particles composing the ring do not have a geosynchronous orbit, but the ring structure itself does.)
A Moving Ring
So rings are composed of things swirling around a planet, but what happens if the plane of the ring moves? That is, the ring is experiencing some kind of precession, just like a wobbly top does.
This is very problematic, and would likely qualify it for not appearing on star charts, as the rotating ring could also appear on every point in the sky!
If the ring's precession lets it wobble just a little, star charts may show its maximum and minimum positions and dates corresponding to those. Oh, this also means that measuring the height/position of the ring becomes another easy way to measure time, so calendars in such a world may be based off of that. (And yes, it may or may not line up well with the actual year, so no, you may not get a perfect calendar. Sorry mathematicians!)
If the ring's precession lets it wobble a lot (as in "twice a year, the ring is directly overhead any point on the globe between really far north and really far south, twice a year."), it ought to be omitted from star charts. You may have a small side-chart showing where the ring would be, and what stars are behind it.