Silicon carbide (SiC) has recently drawn an enormous amount of industrial interest due to its useful mechanical properties, such as its thermal resistance, abrasion resistance and thermal conductivity at high temperatures. In this study, RF thermal plasma (PL-35 Induction Plasma, Tekna CO., Canada) was utilized for the synthesis of high-purity SiC powder from an organic precursor (hexamethyldisilazane, vinyltrimethoxysilane). It was found that the SiC powders obtained by the RF thermal plasma treatment included free carbon and amorphous silica ($SiO_2$). The SiC powders were further purified by a thermal treatment and a HF treatment, resulting in high-purity SiC nano-powder. The particle diameter of the synthesized SiC powder was less than 30 nm. Detailed properties of the microstructure, phase composition, and free carbon content were characterized by X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), a thermogravimetric (TG) analysis, according to the and Brunauer-Emmett-Teller (BET) specific surface area from N2 isotherms at 77 K.