The dipole strength of the nuclide Co59 was studied in photon-scattering experiments using bremsstrahlung produced with electron beams of energies of 8.6 and 12.2 MeV at the bremsstrahlung facility γELBE. We identified 130 levels up to an excitation energy of 10.5 MeV. The quasicontinuum of unresolved transitions was included in the analysis of the spectra and the intensities of branching transitions were estimated on the basis of simulations of statistical γ-ray cascades. The photoabsorption cross section up to the neutron-separation energy was determined and is compared with predictions of the statistical reaction model as well as data for even-mass nuclides in this mass region. The experimental dipole strength function is compared with an M1 strength function obtained from shell-model calculations.