Coupling an ion trap with synchrotron radiation is shown here to be a powerful approach to measure photoionization cross sections on ionic species relaxed in their ground state. The photoionization efficiency curve of Xe+ ions stored in a Fourier transform ion cyclotron resonance ion trap was recorded at ELETTRA in the 20-23 eV photon energy range. Absolute cross sections were derived by comparison of the photoionization yield of Xe+ with measurements from the ASTRID merged-beam experiment. Multiconfiguration Dirac-Fock calculations were performed for the interpretation of these new data.