The invention relates to a copolymer resulting from the polymerization of: (i) 70% to 95% by weight, of the total weight of the monomers, of isobornyl (meth)acrylate; (ii) 1% to 30% by weight of vinylphosphonic acid monomer; (iii) 0 to 20% by weight of an additional monomer. The invention also relates to a cosmetic composition comprising the copolymer and to a cosmetic process for caring for or making up keratin materials, comprising the topical application of the composition to the keratin materials.It also relates to the use of the copolymer as a skin-tensioning agent.