Single-atom manipulation within doped correlated electron systems could help disentangle the influence of dopants, structural defects, and crystallographic characteristics on local electronic states. Unfortunately, the high diffusion barrier in these materials prevents conventional manipulation techniques. Here, we demonstrate the possibility to reversibly manipulate select sites in the optimally doped high-temperature superconductor Bi2Sr2CaCu2O8+x using the local electric field of the tip of a scanning tunneling microscope. We show that upon shifting individual Bi atoms at the surface, the spectral gap associated with superconductivity is seen to reversibly change by as much as 15 milli-electron volts (on average similar to 5% of the total gap size). Our toy model, which captures all observed characteristics, suggests that the electric field induces lateral movement of local pairing potentials in the CuO2 plane.