Human RAD51 is a key protein in the repair of DNA by homologous recombination. Its assembly onto DNA, which induces changes in DNA structure, results in the formation of a nucleoprotein filament that forms the basis of strand exchange. Here, we determine the structural and mechanical properties of RAD51-dsDNA filaments. Our measurements use two recently developed magnetic tweezers assays, freely orbiting magnetic tweezers and magnetic torque tweezers, designed to measure the twist and torque of individual molecules. By directly monitoring changes in DNA twist on RAD51 binding, we determine the unwinding angle per RAD51 monomer to be 45°, in quantitative agreement with that of its bacterial homolog, RecA. Measurements of the torque that is built up when RAD51-dsDNA filaments are twisted show that under conditions that suppress ATP hydrolysis the torsional persistence length of the RAD51-dsDNA filament exceeds that of its RecA counterpart by a factor of three. Examination of the filament's torsional stiffness for different combinations of divalent ions and nucleotide cofactors reveals that the Ca2+ ion, apart from suppressing ATPase activity, plays a key role in increasing the torsional stiffness of the filament. These quantitative measurements of RAD51-imposed DNA distortions and accumulated mechanical stress suggest a finely tuned interplay between chemical and mechanical interactions within the RAD51 nucleoprotein filament.