A new mode of effective interaction of molecular rotational degrees of freedom with an intense, nonresonant, ultrashort laser pulse is explored. Transient nonadiabatic charge redistribution (TNCR) in larger molecules or molecular ions causes impulsive-torque interaction that replaces the traditional mechanism of molecular alignment based on perturbative interaction of the laser field with electronic subsystem as manifested in linear anisotropic polarizability or hyperpolarizability. We explore this new alignment mechanism on a popular generic model of a tight-binding diatomic molecule. We consider the case of rotational wavepacket formation when a molecule is initially in the ground rotational state. The rotational wavepacket emerging from the TNCR interaction consists of states with higher rotational quantum numbers, in comparison with the anisotropic-polarizability case, and the after-pulse alignment oscillations are out-of-phase with those resulting from the traditional interaction. The TNCR interaction mode is expected to play a major role when a strong laser field actually causes extensive nonresonant excitation and/or ionization of a molecule.