This Letter details a measurement of the ionization yield (Q(y)) of 6.7 keV(40)Ar atoms stopping in a liquid argon detector. The Q(y) of 3.6-6.3 detected e(-)/keV, for applied electric fields in the range 240-2130 V/cm, is encouraging for the use of this detector medium to search for the signals from hypothetical dark matter particle interactions and from coherent elastic neutrino-nucleus scattering. A significant dependence of Q(y) on the applied electric field is observed and explained in the context of ion recombination.