The modification of achira starch a thermoplastic biopolymer is shown. Glycerol and sorbitol, common plasticizers, were used in the molten state with organic acids such as oleic acid and lactic acid obtaining thermodynamically more stable products. The proportion of starch:plasticizer was 70:30, and the acid agent was added in portions from 3%, 6%, and 9% by weight. These mixtures were obtained in a torque rheometer for 10 min at 130 °C. The lactic acid managed to efficiently promote the gelatinization process by increasing the available polar sites towards the surface of the material; as a result, there were lower values in the contact angle, these results were corroborated with the analysis performed by differential scanning calorimetry and X-ray diffraction. The results derived from oscillatory rheological analysis had a viscous behavior in the thermoplastic starch samples and with the presence of acids; this behavior favors the transitions from viscous to elastic. The mixture of sorbitol or glycerol with lactic acid promoted lower values of the loss module, the storage module, and the complex viscosity, which means lower residual energy in the transition of the viscous state to the elastic state; this allows the compounds to be scaled to conventional polymer transformation processes.