  High-field electrical transport and point-contact tunneling spectroscopy were
used to investigate superconducting properties of the unique spinel oxide,
LiTi$_2$O$_{4-\delta}$ films with various oxygen content. We find that the
upper critical field $B_\mathrm{c2}$ gradually increases as more oxygen
impurities are brought into the samples by carefully tuning the deposition
atmosphere. It is striking that although the superconducting transition
temperature and energy gap are almost unchanged, an astonishing isotropic
$B_\mathrm{c2}$ up to $\sim$ 26 Tesla is observed in oxygen-rich sample, which
is doubled compared to the anoxic sample and breaks the Pauli limit. Such
anomalies of $B_\mathrm{c2}$ were rarely reported in other three dimensional
superconductors. Combined with all the anomalies, three dimensional spin-orbit
interaction induced by tiny oxygen impurities is naturally proposed to account
for the remarkable enhancement of $B_\mathrm{c2}$ in oxygen-rich
LiTi$_2$O$_{4-\delta}$ films. Such mechanism could be general and therefore
provides ideas for optimizing practical superconductors with higher
$B_\mathrm{c2}$.

Superconductivity