Spacetime curvature of the Earth deforms wavepackets of photons sent from the Earth to satellites, thus influencing the quantum state of light. We show that Gaussian steering of photon pairs, which are initially prepared in a two-mode squeezed state, is affected by the curved spacetime background of the Earth. We demonstrate that quantum steerability of the state increases for a specific range of height $h$ and then gradually approaches a finite value with further increasing height of the satellites orbit. Comparing with the peak frequency parameter, the Gaussian steering changes more for different squeezing parameters, while the gravitational frequency effect leads to quantum steering asymmetry between the photon pairs. In addition, we find that the influence of spacetime curvature on the steering in the Kerr spacetime is very different from the non-rotating case because special relativistic effects are involved.
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