The current race in quantum communication, endeavouring to establish a global quantum network, must account for special and general relativistic effects. For example, Shapiro time-delay, gravitational lensing, and frame dragging -all due to how a mass distribution alters geodesics -are well-studied. Here, we report how the curvature of spacetime geometry affects the propagation of information carriers along an arbitrary geodesic. An explicit expression for the distortion onto the carrier wavefunction in terms of the Riemann curvature is obtained. Furthermore, we investigate this distortion for anti de Sitter and Schwarzschild geometries. For instance, the spacetime curvature causes a 0.11 radian phaseshift for communication between Earth and the International Space Station on a monochromatic laser beam as well as quadrupole astigmatism, which causes 13.4% crosstalk among the modes, when structured modes traverse through the solar system. Our finding shows that this gravitational distortion is significant, and it needs to be either pre-or post-corrected at the sender or receiver to retrieve the information.