SiC nanorods were synthesized by a reaction at a temperature of 1200 degrees C, under an argon gas atmosphere, from silicon and amorphous carbon powders mixed by ball milling. The reaction product, which contain SiC nanorods and nanoparticles, has been characterized by high-resolution transmission electron microscopy, X-ray diffraction, and micro-Raman spectroscopy. The synthesized nanorods are more than 1 micron long with a mean diameter of about 10-30 nm. The nanorods possess a well-defined crystalline structure with a thin layer of amorphous SiO2 on the surface. Raman shifts of SiC nanorods and the role of structural defects are discussed.