A new experimental design for alpha-particle irradiation of cells in vitro is described where the alpha-particle irradiator is based on a 210Po radioactive source. In the described set-up cells are grown directly on an alpha-particle detector and irradiation is done from below. For an irradiated cell dish the number of alpha-particle traversals through each individual cell is scored by using retrospective track etch dosimetry and an accurate technique for individual cell relocation. Calibration experiments characterizing the new irradiator system are presented.