The report describes the synthesis of degradable, pH-sensitive, membrane-destabilizing, star-shaped polymers where copolymers of hydrophobic hexyl methacrylate (HMA) and 2-(dimethylamino)ethyl methacrylate (DMAEMA) monomers are grafted from the secondary face of a beta-cyclodextrin (β-CD) core via acid-labile hydrazone linkages using atom transfer radical polymerization. The effect of the graft's molecular weight, HMA/DMAEMA molar ratio, and the fraction of DMAEMA converted to cationic N,N,N-trimethylaminoethyl methacrylate (TMAEMA) monomers on polymer's transfection capacity is systematically investigated. Results show that all star-shaped polymers condense anti-GAPDH silencing RNA (siRNA) into nanosized particles at +/- ratio ≤ 4:1. Star polymers with shorter (25kDa) P(HMA-co-DMAEMA-co-TMAEMA) grafts are more efficient and less cytotoxic than carriers with longer (40kDa) grafts. The results show that increasing the ratio of hydrophobic HMA monomers in graft's composition higher than 50 mole% dramatically reduces polymer's aqueous solubility and abolishes their transfection capacity. Further, retention of DMAEMA monomers in graft's composition provide a buffering capacity that enhanced the endosomal escape and transfection capacity of the polymers. These systematic studies show that β-CD-P(HMA-co-DMAEMA-co-TMAEMA)4.8 polymer with a 25 kDa average graft's molecular weight and a 50/25/25 ratio of HMA/DMAEMA/TMAEMA monomers is the most efficient carrier in delivering the siRNA cargo into the cytoplasm of epithelial cancer cells.