The directional correlations of gamma transitions in ¹⁰⁵Rh have been measured from the beta ^- decay of 4.4 h ¹⁰⁵Ru utilising a Ge(Li)-Na(Tl) spectrometer. The present results, which include measurements on six gamma cascades not studied previously, when combined with other available data establish spin and parity assignments for the majority of low-lying levels in ¹⁰⁵Rh up to about 1 MeV. The multipole mixing ratios delta (E2/M1) calculated from the measured angular correlations are presented.