Yes, we can. However, we cannot make enough ozone to replace the amount which is being destroyed in the upper atmosphere. But regarding small quantities, it is possible.
The conversion reaction which implies oxygen molecules and gives ozone molecules occurs when the oxygen is ionized. There are several possibilities of creating artificial ozone.
An efficient method is using a corona discharge tube,Vacuum-ultraviolet ozone generators require less money, but they are less efficient.
During the cold plasma method, the oxygen is split into atoms, then it recombines and forms ozone molecules.
The electrolytic method creates 20-30% ozone, but it is not very reliable. During the process, the water is dissociated into oxygen, hydrogen and ozone. The first two gases are removed, since the superior ozone concentration.