We studied structural changes in a 5 unit cell thick La1.96Sr0.04CuO4 film, epitaxially grown on a LaSrAlO4 substrate with a single unit cell buffer layer, when ultra-high electric fields were induced in the film by applying a gate voltage between the film (ground) and an ionic liquid in contact with it. Measuring the diffraction intensity along the substrate-defined Bragg rods and analyzing the results using a phase retrieval method we obtained the three-dimensional electron density in the film, buffer layer, and topmost atomic layers of the substrate under different applied gate voltages. The main structural observations were: (i) there were no structural changes when the voltage was negative, holes were injected into the film making it more metallic and screening the electric field; (ii) when the voltage was positive, the film was depleted of holes becoming more insulating, the electric field extended throughout the film, the partial surface monolayer became disordered, and equatorial oxygen atoms were displaced towards the surface; (iii) the changes in surface disorder and the oxygen displacements were both reversed when a negative voltage was applied; and (iv) the c-axis lattice constant of the film did not change in spite of the displacement of equatorial oxygen atoms.