We present an ultrasensitive absorption spectrometer based on a 30 Hz/s stability, sub-kHz line width laser source coupled to a high-stability cavity-ring-down-spectroscopy setup. It provides direct and precise measurements of the isotopic ratios δ17O and δ18O in CO2. We demonstrate the first optical absorption measurements of 17O anomalies in CO2 with a precision better than 10 ppm, matching the requirements for paleo-environmental applications. This illustrates how optical absorption methods have become a competitive alternative to state-of-the-art isotopic ratio mass spectrometry techniques.