  We demonstrate a new spectroscopic method for studying electronic transitions
in molecules with extremely broad range of angular momentum. We employ an
optical centrifuge to create narrow rotational wave packets in the ground
electronic state of $^{16}$O$_2$. Using the technique of resonance-enhanced
multi-photon ionization, we record the spectrum of multiple ro-vibrational
transitions between $X^3\Sigma_{g}^{-}$ and $C^3\Pi_{g}$ electronic manifolds
of oxygen. Direct control of rotational excitation, extending to rotational
quantum numbers as high as $N\gtrsim 120$, enables us to interpret the complex
structure of rotational spectra of $C^3\Pi_{g}$ beyond thermally accessible
levels.
