We measure cross-beam energy transfer (CBET) saturation by ion heating in a gas-jet plasma characterized using Thomson scattering. A wavelength-tunable ultraviolet (UV) probe laser beam interacts with four intense UV pump beams to drive large-amplitude ion-acoustic waves. For the highest-intensity interactions, the power transfer to the probe laser drops, demonstrating ion-acoustic wave saturation. Over this time, the ion temperature is measured to increase by a factor of 7 during the 500-ps interaction. Particle-in-cell simulations show ion trapping and a subsequent ion heating consistent with measurements. Linear kinetic CBET models are found to agree well with the observed energy transfer when the measured plasma conditions are used.