β-cyclodextrin (CD) derivatives containing aromatic triazole ring were studied as potential carriers of drugs containing an anthraquinone moiety in the structure: anthraquinone-2-sulfonic acid (AQ2S), anthraquinone-2-carboxylic acid (AQ2CA) and a common anthracycline, daunorubicin (DNR). UV-Vis and voltammetry measurements were carried out to determine the solubilities and stability constants of the complexes formed and revealed the unique properties of the chosen CDs as effective pH dependent drug complexing agents. The stability constants of the drug complexes with the CDs containing triazole: βCDLip and βCDGAL were significantly larger than with the native βCD. The AQ2CA and AQ2S drugs are ill-soluble and their solubilities increased as the result of complex formation with βCDLip and βCDGAL ligands. AQ2CA, AQ2S were negatively charged at pH 7.4 and therefore they were less prone to form inclusion complex with the hydrophobic CD cavity than at pH 3 (characteristic of gastric juices) when they were protonated. βCDTriazole and βCDGAL ligands were found to form weaker inclusion complexes with the positively charged drug DNR at acidic pH (pH 5.5) than in the neutral medium (pH 7.4) when the drug dissociates to the neutral, uncharged form. This pH dependence is favorable for anti-tumor applications.