We study the propagation of light under a strong electric field in Born–Infeld electrodynamics. The nonlinear effect can be described by the effective indices of refraction. Because the effective indices of refraction depend on the background electric field, the path of light can be bent when the background field is non-uniform. We compute the bending angle of light by a Born–Infeld-type Coulomb charge in the weak lensing limit using the trajectory equation based on geometric optics. We also compute the deflection angle of light by the Einstein–Born–Infeld black hole using the geodesic equation and confirm that the contribution of the electric charge to the total bending angle agree.