Reinforced concrete is an essential material in the modern world, and the use of genetic algorithms that aim at the optimization of the structures of this material is an increasingly widespread tool. The objective of the present work was to propose a method by means of a Genetic Algorithm to find the optimized geometry of a rectangular reinforced concrete column based on its cost. The two main parts of the work were developed as: a geometry verification algorithm that received height, base, layers in x and y directions, diameters of transverse and longitudinal steel rebar as the main parameters of the proposed sections, and a genetic algorithm that generated 240 random populations and selected them, crossed among them and then generated new 100 generations of individuals, followed by selection of optimized ones by its penalized cost. The generations had more and more favorable individuals and it was possible to determine an optimized geometry for the proposed example. It is, therefore, concluded that genetic algorithms are useful tools for optimizing reinforced concrete parts with multiple parameters. The proposed algorithm methodology really checks and selects the best individuals for the sections proposed by engineers, and larger initial populations are essential to find a minimum global cost among the different options.