A method for synthesizing carbon nanotube drug carriers and the carbon nanotube drug carriers are disclosed. Initially, carbon nanotubes, nitric acid, and sulfuric acid are mixed to oxidize carbon nanotubes in a first mixture. The oxidized carbon nanotubes are then extracted from the first mixture. The oxidized carbon nanotubes and monohydrated citric acid are mixed to synthesize carbon nanotubes grafted with poly(citric acid) in a second mixture. The carbon nanotubes grafted with poly(citric acid) are then extracted from the second mixture. The carbon nanotubes grafted with poly(citric acid) and 4-(dimethylamino)pyridine are dissolved in anhydrous dimethylformamide in a third mixture. Next, a mixture that comprises a drug is added to the third mixture to synthesize the carbon nanotubes grafted with poly(citric acid) and the drug in a fourth mixture. Then, the carbon nanotubes grafted with poly(citric acid) and the drug are extracted from the fourth mixture.