Résumé : In-source resonance ionization spectroscopy of the neutron-rich actinium isotopes Ac225-229 has been performed at the ISAC facility in TRIUMF, probing a D3/22→P5/2-4 atomic transition. New data on the magnetic dipole moments and changes in mean-square charge radii δ(r2) of Ac226,228,229 have been obtained. The comparison of the measured isotope shifts and magnetic dipole coupling constants a(P5/2-4) of Ac225,227 with a high-resolution data set is used to identify systematic uncertainties on the deduced δ(r2)A,215 and magnetic dipole moment values. The charge radii odd-even staggering is evaluated for the odd-N isotopes, showing that Ac226 has an inverted odd-even staggering that might be linked with a reflection-asymmetric shape. Comparison of the magnetic dipole moments of Ac225,227,229 with Nilsson-model estimates supports the assumption of octupole deformation in isotopes Ac225,227 and its gradual decrease toward isotope Ac229. The changes in mean-square charge radii are compared to self-consistent calculations employing multiple modern energy density functionals: SLy5s1, BSk31, and DD-MEB1. For SLy5s1 in particular, self-consistent time-reversal breaking calculations of odd-odd nuclei incorporating finite octupole deformation are reported for the first time. For these calculations, the overall best agreement is obtained when the octupole degree of freedom is taken into account.