We show how the rotational quantum state of a linear or symmetric top rotor can be reconstructed from finite time observations of the polar angular distribution under certain conditions. The presented tomographic method can reconstruct the complete rotational quantum state in many nonadiabatic alignment experiments. Our analysis applies for measurement data available in principle with existing measurement techniques. In practice, a full reconstruction requires a large amount of data and is thus experimentally challenging. Nonetheless, showing that the necessary information is present, we substantiate the use of approximate reconstruction methods with such data.