While electron transfer reactions typically occur at the interface between a reactant and a metal in an electrolyte solution, it is also possible to initiate these reactions at the interface between a plasma (gas discharge) and a solution. In this case, a free, gaseous electron is injected into the solution from the plasma phase, solvating before reacting away. In our previous work, we have shown that an atmospheric pressure plasma in argon can be used as a cathode in an electrolytic cell to produce solvated electrons[1]. In this work, we show that the solvated electrons produced by the plasma cathode can be used to reduce dissolved carbon dioxide, CO_2(aq), to form the carboxyl radical anion, CO₂^–_(aq). The CO₂^–_(aq) radical can either recombine to form oxalate under basic conditions or react with H⁺_(aq) to produce formate under acidic conditions.  We measure the Faradaic yield of both oxalate and formate formation using liquid ion chromatography and show that it is dictated by the well-known reaction kinetics of solvated electrons and CO₂^–_(aq).  Importantly, these 3-dimensional reaction kinetics are distinct from the 2-dimensional kinetics found in traditional electrochemistry and catalysis, and may open up new opportunities to explore electrochemical carbon dioxide reforming.