We present fiber Bragg gratings (FBGs) fabricated using adaptive optics aberration compensation for the first time to the best of our knowledge. The FBGs are fabricated with a femtosecond laser by the point-by-point method using an air-based objective lens, removing the requirement for immersion oil or ferrules. We demonstrate a general phase correction strategy that can be used for accurate fabrication at any point in the fiber cross-section. We also demonstrate a beam-shaping approach that nullifies the aberration when focused inside a central fiber core. Both strategies give results which are in excellent agreement with coupled-mode theory. An extremely low wavelength polarization sensitivity of 4 pm is reported.