  Spinel oxides are well-known functional materials but rarely show
superconductivity. Recently, emergent superconductivity was discovered in
MgTi$_2$O$_4$, which is attributed to the increase of electron doping and the
suppression of orbital order. Here, we utilized Ti $L$-edge resonant inelastic
X-ray scattering to study the orbital excitations in superconducting (SC) and
insulating MgTi$_2$O$_4$ films. We find that the spectral weight of orbital
excitations is enhanced and the energy of $t_{2g}$ intra-band excitation is
softened in the SC film compared to the insulating one, suggesting higher
electron doping and suppressed orbital order gap in the SC sample. These
observations were further supported by our multiplet calculations using minimal
two-site model. Our results provide spectroscopic evidence for the competition
between orbital order and superconductivity in MgTi$_2$O$_4$ and shed light on
searching for novel superconductors in spinel oxides.
