We study theoretically the action of subcycle unipolar pulses on the rotational dynamics of polar molecules. We show that efficient excitation of molecular rotational resonances by subcycle pump pulses with respect to bipolar single-cycle one is achieved, provided that duration of excitation pulses is much smaller than the rotational period of the molecule. The excitation probability for different rotational levels is analysed in dependence on the parameters of molecules and pump pulses. Remarkably, our analysis revealed the possibility of the almost single level excitation and the formation of the population inversion in the rotational levels excited by unipolar pulses, in spite of the nonresonant interaction and ultrabroad spectrum of subcycle pulses. This approach is entirely different from the traditional resonant excitation techniques with long quasi-monochromatic pulses tuned to the molecular transition. And from the other methods, when multi-color laser pulses or single-cycle THz pulses are used for control of the molecular properties. This opens new avenues in applications related to control of molecular systems and lasing creation, since it allows efficient ultrafast control over different rotational levels.