The ionization signals in the liquid argon of the ATLAS electromagnetic calorimeter are studied in detail using cosmic muons. In particular, the drift time of the ionization electrons is measured and used to assess the intrinsic uniformity of the calorimeter gaps and estimate its impact on the constant term of the energy resolution. The drift times of electrons in the cells of the second layer of the calorimeter are uniform at the level of 1.3\% in the barrel and 2.8\% in the endcaps. This leads to an estimated contribution to the constant term of (0.29(-0.04)(+0.05))\% in the barrel and (0.54(-0.04)(+0.06))\% in the endcaps. The same data are used to measure the drift velocity of ionization electrons in liquid argon, which is found to be 4.61 +/- 0.07 mm/mu s at 88.5 K and 1 kV/mm.