We have studied the growth of a SrTiO3 shell on self-catalyzed GaAs nanowires grown by vapor-liquid-solid assisted molecular beam epitaxy on Si(111) substrates. To control the growth of the SrTiO3 shell, the GaAs nanowires were protected using an arsenic capping/decapping procedure in order to prevent uncontrolled oxidation and/or contamination of the nanowire facets. Reflection high energy electron diffraction, scanning electron microscopy, transmission electron microscopy, and X-ray photoelectron spectroscopy were performed to determine the structural, chemical, and morphological properties of the heterostructured nanowires. Using adapted oxide growth conditions, it is shown that most of the perovskite structure SrTiO3 shell appears to be oriented with respect to the GaAs lattice. These results are promising for achieving one-dimensional epitaxial semiconductor core/functional oxide shell nanostructures.