Undoped and Fe-doped (0.35, 0.5 and 0.7 at% Fe) LiNbO3 single-crystal fibers were grown using the micro-pulling-down method with resistivity heating. The fibers chemical homogeneity was examined with electron probe micro-analysis and crystallographic orientation was checked with Raman spectroscopy. The engraving of an optical waveguide in a Fe-doped LiNbO3 single-crystal fiber was performed with an optical vortex beam, which creates a guiding core in the fiber with an increase of the refractive index via the photorefractive effect presents in lithium niobate. This waveguide was tested by probe beams at 633 and 1550nm.