This study reports the dry reforming of methane (DRM) using non-thermal plasma in a swirl-induced point-plane electrode discharge reactor to produce syngas. This reactor geometry facilitates better mixing of the reactant gases in the plasma region, thus increasing the residence time and conversion of the reactants. The effect of varying flow rates and compositions of CO2/CH4 (v%/v%) on conversion was studied. A high-voltage AC power input of 50 W and 70 W at a frequency of 19 kHz was provided. The voltage−current characteristics with respect to time were studied. The results show that with an increase in the flow rate of the gas mixture from 0.5 to 2 LPM the conversion of both CO2 and CH4 decreases, while an increase in the concentration of CO2 or CH4 (from 25 to 75%) increases the conversion of the respective reactant. The products, viz. syngas (CO and H2), C2 hydrocarbons, and solid carbon, were characterized and quantified. The maximum total conversion of 44% was obtained for a CO2:CH4 ratio of 25:75 (v%/v%) at a flow rate of 0.5 LPM. The solid carbon collected from the reactor walls was analyzed, and it was found to be 89.9% pure with traces of oxygen functionality. The increase in flow rate decreased the specific energy input, which eventually resulted in lowering the energy cost.