We have investigated the ability of AGATA triple clusters to measure the linear polarization of gamma rays, exploiting the azimuthal-angle dependence of the Compton scattering differential cross section. To this aim, partially polarized gamma rays have been produced by Coulomb excitation of the first excited state of 104Pd and 108Pd, which decay to the ground state by emission of gamma rays of 555.8 keV and 433.9 keV, respectively. Pulse-shape analysis and gamma-ray tracking techniques have been used to determine the position and time sequence of the interaction points inside the germanium crystals. Anisotropies in the detection efficiency have been taken into account using 661.6 keV gammas from a 137Cs radioactive source. We obtain an average analyzing power of 0.451(34) at 433.9 keV and 0.484(24) at 555.8 keV.