The ability to shape the index profile of optical fibers holds the key to fully flexible engineering of their optical properties and future applications. We present a new approach for the development of a graded index fused silica fiber based on core nanostructurization. A graded index core is obtained by means of distribution of two types of subwavelength glass rods. The proposed method allows to obtain arbitrary graded distribution not limited to the circular or any other symmetry, such as in the standard graded index fibers. We have developed a proof of concept fiber with parabolic refractive index core and showed a perfect match between its predicted, designed and measured properties. The fiber has a core composed of 2107 rods of 190 nm of diameter made of either pure fused silica or Ge-doped fused silica with 8.5% mol concentration. The proposed method breaks the limits of standard fabrication approaches used in fused silica fiber technology.