  The rapidly rotational motion of C$_{60}$ molecules provides us with an
ingenious way to test Mashhoon's spin-rotation coupling. The spin-rotation
coupling of electrons in the rotating C$_{60}$ molecule is considered in the
present letter. It is shown that the intrinsic spin (gravitomagnetic moment) of
the electron that can be coupled to the time-dependent rotating frequency of
rotating frame of reference (C$_{60}$ molecule) results in a geometric phase,
which may be measured through the electronic energy spectra of C$_{60}$
molecules.
