We report the detection of 13C17O and present observations of three additional rare CO isotopomers made toward core C of the ρ Ophiuchi molecular cloud. The data encompass single-pointed observations of the J=1-->0 and J=2-->1 rotational transitions for C18O, C17O, 13C17O, and the J=1-->0 transition for 13C18O. Emission is detected for all isotopes and transitions observed. For the two 17O-containing species, the interstellar spectra display a partially resolved hyperfine spectrum due to the I=5/2 spin of the 17O nucleus. The isotope abundance ratios derived from these measurements are [12C]/[13C]=65.0+/-6.3(stat)+/-9.2(syst) and [18O]/[17O]=4.15+/-0.52(stat)+/-0.59(syst), consistent with recent measurements for nearby molecular clouds. Thus, our measurements support the idea that both ratios are smaller in the local interstellar medium (ISM) than their terrestrial values of 89 and 5.5. Based on observations collected at the European Southern Observatory, Chile (ESO 66.C-0143).