Pressure measurement is often the limiting factor in the accuracy of quantitative ion-molecule experiments. We present a new method for pressure measurement based on analysis of pressure-limited Fourier transform ion cyclotron resonance (FTICR) linewidths for well-characterized collisions of Ar+ with Ar. The kinetic energy dependence of Ar+/Ar collision cross sections is well-described using a single-parameter fitting procedure, which results in pressure measurements in good agreement with those from a cold cathode tube and from measurement of total ion signal following electron impact ionization. The new method avoids problems inherent in ionization-based methods, such as those arising from differences in ionization potential or perturbations to the pressure that occur during electron ionization of the gas to be measured, and should be applicable in the trapping cells of FTICR and Orbitrap mass spectrometers.