The realization of a Fabry-Pérot (F-P) cavity based on a Ti :LiNbO3 optical waveguide obtained by using a concept which consists of milling the Bragg gratings (BGs) in the cavity by the focused ion beam technique is shown in this letter. This F-P cavity is formed by two BGs which represent the two reflecting mirrors of the interferometer. The length of the cavity is defined by the distance between the two BGs. Thirty-one peaks and a free spectral range FSR=1.75nm have been experimentally obtained in the range of wavelengths [1505-1548]. The experimental results are in accordance with those of theory. The fabrication process, the experimental results, as well as improvements to increase finesse F and FSR are discussed.