Thought experiment on space curvature due to gravity Let's say you built a huge, straight rigid beam out in space, far from the sun (outside the orbit of Pluto).  It is very long, say 200,000 miles long, but can be very narrow.
Then you move it to the Earth's orbit, and align it such that it's center point is on the orbit of the earth, and the beam is along the tangent line of the orbit at this point.
At this position, is the beam curved?  Does the curved-space that guides the Earth orbit actually curve this beam, such that it would NOT be a tangent, but an arc of the orbit?
Could this curvature be observed if one way far away, say above the plane of the orbit and looking down on it?
 A: No, the straight beam will not magically turn into a curved beam.
I suspect you have a slightly confused idea of what the curvature of spacetime means physically. Basically it means that a freely moving body will appear to accelerate relative to some distant observer. Conversely if we want stop the body from accelerating then we have to apply a force (i.e. the gravitational force).
Suppose instead of a rigid beam you had a long length of something floppy like string. If you tied the middle of the string to the Earth and stretched either side out along the Earth's orbit then there would be an equilbrium configuration with the string arranged in an arc as you describe (actually I suspect this would be an unstable equilibrium, though I'd need to think some more about it).
If you go back to your rigid beam the rigidity of the beam stops it moving freely, and as a result there will be a bending force on the beam. Classically this would be a tidal force due to gravity being stronger in the middle of the beam than at its ends.
