Production cross-sections of the therapeutic ¹⁰⁵Rh radionuclide from proton-induced reactions on natural palladium target were measured using stacked-foil activation technique combined with high resolution 𝛾-ray spectrometry at the MC50 cyclotron of the Korea Institute of Radiological and Medical Sciences. Note that cyclotron production of the ¹⁰⁵Rh radionuclide from natural palladium target was measured here for the first time. Results are compared with the theoretical values obtained using the model codes TALYS and ALICE-IPPE. Thick target integral yields for the investigated ¹⁰⁵Rh radionuclide were deduced from the threshold energy to 40 MeV. Measured data of the ¹⁰⁵Rh radionuclide are important because of its potential applications in nuclear medicine and/or therapeutic purposes. Optimal production circumstances for the therapeutic ¹⁰⁵Rh radionuclide using a cyclotron are discussed elaborately.