Copper is an important metal both in living organisms and in the industrial activity of humans, it is also a distributed water pollutant and a toxic agent capable of inducing acute and chronic health disorders. There are several fluorescent chemosensors for copper (II) determination in solutions; however, they are often difficult to synthesize and solvent-sensitive, requiring a non-aqueous medium. The present paper improves the known analytical technique for copper (II) ions, where the linear dependence between the ascorbic acid oxidation rate constant and copper (II) concentration is used. The limits of detection and quantification of the copper (II) analysis kinetic method are determined to be 82 nM and 275 nM, respectively. In addition, the selectivity of the chosen indicator reaction is shown: Cu2+ cations can be quantified in the presence of the 5–20 fold excess of Co2+, Ni2+, and Zn2+ ions. The La3+, Ce3+, and UO22+ ions also do not catalyze the ascorbic acid oxidation reaction. The effect of the concentration of the common background electrolytes is studied, the anomalous influence for chloride-containing salts is observed and discussed.