  Since about ten years ago, varying $\alpha$ theories attracted many
attentions, mainly due to the first observational evidence from the quasar
absorption spectra that the fine structure ``constant'' might change with
cosmological time. In this work, we investigate the cosmic evolution of
$\alpha$ driven by the Dirac-Born-Infeld (DBI) scalar field. To be general, we
consider various couplings between the DBI scalar field and the electromagnetic
field. We also confront the resulting $\Delta\alpha/\alpha$ with the
observational constraints, and find that various cosmological evolution
histories of $\Delta\alpha/\alpha$ are allowed. Comparing with the case of
varying $\alpha$ driven by quintessence, the corresponding constraints on the
parameters of coupling have been relaxed, thanks to the relativistic correction
of the DBI scalar field.
