General relativity assumes that space itself is warped by gravity, which is what gives rise to the shapes of the paths followed by objects subject to a gravitational field.
If space itself truly bends, then the paths of all particles in an area of space warped by a gravitational field should be affected.
As a result, the path of the force carrier of an electrostatic field should also be affected by the presence of a gravitational field, since the path of that force carrier should also be affected by the local warping of space.
Therefore, any electrostatic field that is within an area of space warped by a gravitational field should in some way be affected the presence of the gravitational field.
If so, has the effect been measured by experimentation?