New copolymers of methyl acrylate with 1-vinylimidazole, 1-vinyl-1,2,4-triazole, and 4-vinyl-1,2,3-triazole are synthesized by radical copolymerization. It is shown that the reactivity ratios for methyl acrylate and 1-vinylimidazole are 0.83 ± 0.09 and 0.25 ± 0.02, for methyl acrylate and 1-vinyl-1,2,4-triazole are 1.0 ± 0.04 and 0.27 ± 0.01, and for methyl acrylate and (4-vinyl-1Н-1,2,3-triazolyl)-methyl pivalate are 0.56 ± 0.03 and 2.90 ± 0.20, respectively. The behavior of the copolymers in aqueous media and their thermoresponsive properties are studied by potentiometric titration and dynamic light scattering. Copolymer macromolecules occur in aqueous solutions in the form of large associates the fraction of which increases upon heating; in some cases, an insoluble phase is formed. It is found that the copolymers with the grafted oligopropylamine moieties containing N-vinylazole units can interact with the DNA oligonucleotide, stimulating their research as agents for the delivery of nucleic acids to living cells.