As citric acid decomposes in its melting point, polycondensation of this monomer to prepare its polymers and copolymers is not possible. This study describes a feasible way to synthesize hyperbranched polyesters consisting of citric acid and glycerol monomers. In the first strategy, different ratios of citric acid and glycerol as AB3 and A3 monomers were mixed and heated step by step to avoid decomposition of citric acid. The produced water, as byproduct of polycondensation, was removed from the mixture by vacuum pump. Synthesized hyperbranched copolymers were characterized by nuclear magnetic resonance, gel permeation chromatography, thermogravimetric analysis, and dynamic light scattering. Ability of the synthesized hyperbranched polyesters to load and transfer cisplatin as an anticancer drug was investigated and it was found that their loading capacity is high and the prepared drug delivery systems are stable in saline buffer for several months. The toxicity of anticancer drug delivery systems against C26 cancer cell line was evaluated. Cisplatin loaded in polyesters showed lower IC50 value than the free cisplatin, confirming the efficacy of the synthesized citric acid–glycerol hyperbranched polyesters as biocompatible cargos to transport anticancer drugs.