Assuming your planet has a similar equatorial bulge to Earth, yes.
If you don't mind your "polar" ring being a few degrees off exactly 90% inclination from the planet's equator, anyway (and this will vary slightly depending on the planet's axial tilt and the inclination of any major moon or moons).
Put the ring in a sun-synchronous orbit. For Earth, this is an orbit with a 300 km or higher perigee (minimum altitude), 93-97 degrees inclincation (i.e. slightly retrograde compared to a true polar orbit) and eccentricity of .02 to .04. Any individual satellite in that orbit around Earth will precess its orbit (due to Earth's equatorial bulge and the eccentricity of the orbit) at exactly the same rate the Earth travels around the sun, keeping the orbit in the same orientation relative to the sun for a prolonged time (not forever, because the orbit will eventually decay, but for multiple years).
These orbits are used in the real world to ensure a satellite has constant solar power (when orbiting over the twilight line), or to ensure (for instance) passing over the noon line on every orbit (handy for photographic purposes, to make map photos with minimum shadows).
Bad news is, those cables connecting your beads can't be taut. If they're loose and stay that way, fine and good, but if they come tight, the ring will start to act like a rigid body and will be unstable as a whole. Better, in fact, to leave them unconnected and give each individual satellite some limited ability to counter orbital decay, if you want it to last decades instead of years.