We describe a high-precision method for measuring pressure shifting of absorption lines. The technique involves the acquisition of high-resolution spectra using a cavity ring-down spectrometer whose length is continuously locked to a frequency-stabilized reference laser over a range of sample pressures. We discuss a relatively large correction arising from the pressure-dependence of dispersion in the cavity modes, and we demonstrate pressure shifting measurements in air for transitions in the 16O2 A-band. Pressure shifts in the range -0.011 to -0.007cm-1atm-1 are reported. We measured relative positions of line centers to within 70kHz and determined pressure shifting coefficients over a 5kPa pressure range with relative uncertainties approximately equal to 1.0%, which constitutes a five-fold improvement over previous measurements.