The dynamics of rotational wave packets of laser-aligned linear molecules were studied with femtosecond laser-driven strong-field ionization (SFI). The dynamics were observed as a function of the delay between a femtosecond probe pulse and a linearly polarized aligning pump pulse. The induced nonadiabatic molecular alignment was directly monitored by the total SFI yield. The measured revival signatures were compared to the calculated degree of molecular alignment taking into account the effects of electronic structure and symmetry of the molecules. By fitting the calculated alignment parameter to the measured experimental data, we also determined the molecular rotational constants of N-2, CO, O-2, and C2H2 gas molecules.