We report on the measurement of the instantaneous Kerr nonlinearity and the retarded alignment of air molecules CO2, N-2, and O-2 triggered by an intense, lambda-cubic terahertz pulse, a diffraction-and transform-limited single-cycle pulse. The strong-field, impulsive low-frequency excitation (3.9 THz) leads to field-free alignment dynamics of these molecules thanks to the terahertz-induced transient dipole moments in the otherwise non-polar molecules. The strong coupling to the terahertz electric transient results in the excitation of coherent large amplitude long-living rotational states at room temperature and ambient pressure. Beyond fundamental investigations of nonlinear properties in gases, our results suggest a route towards field-free molecular alignment at laser intensity well below the ionization threshold. (C) 2015 AIP Publishing LLC.