The tapering of silicon optical fibers is demonstrated using a fusion splicer. The silicon fibers are fabricated using a high pressure chemical deposition technique to deposit an amorphous silicon core inside a silica capillary and the tapering is performed in a separate post-process. Optical and material characterization has revealed a smooth transition region leading to a uniform tapered waist that are both simultaneously crystallized to yield a solid polysilicon core. The strong mode confinement and low taper loss measured in the silicon fibers verifies this tapering approach for the fabrication of structures with nanoscale core dimensions.