The Rare-RI Ring (R3) is a recently commissioned cyclotron-like storage ring mass spectrometer dedicated to mass measurements of exotic nuclei far from stability at Radioactive Isotope Beam Factory (RIBF) in RIKEN. The first application of mass measurement using the R3 mass spectrometer at RIBF is reported. Rare isotopes produced at RIBF, 127 Sn, 126 In, 125 Cd, 124 Ag, 123 Pd, were injected in R3. Masses of 126 In, 125 Cd, and 123 Pd were measured and the mass uncertainty of 123 Pd was improved. The impact of the new 123 Pd result on the solar r-process abundances in a neutron star merger event is investigated by performing reaction network calculations of 20 trajectories with varying electron fraction Ye. It is found that the neutron capture cross section on 123 Pd increases by a factor of 2.2 and β-delayed neutron emission probability, P1n, of 123 Rh increases by 14%. The neutron capture cross section on 122 Pd decreases by a factor of 2.6 leading to pileup of material at A = 122, thus reproducing the trend of the solar r-process abundances. Furthermore, the nuclear deformation predicted to reach its maximum before N = 82 in the Pd isotopic chain is examined. The new mass measurement shows no evidence of such large deformation, though, experimental uncertainty should be further improved to draw a definitive conclusion. This is the first reported measurement with a new storage ring mass spectrometery technique realized at a heavy-ion cyclotron and employing individual injection of the pre-identified rare nuclei. The latter is essential for the future mass measurements of the rarest isotopes produced at RIBF.