  Cosmography is a phenomenological and relatively model-independent approach
to cosmology, where physical quantities are expanded as a Taylor series in the
cosmological redshift, or in related variables. Here we apply this methodology
to constrain possible cosmological variations of the fine-structure constant,
$\alpha$. Two peculiarities of this case are the existence of high-redshift
data, and the fact that one term in the series is directly and tightly
constraint by local laboratory tests with atomic clocks. We use this atomic
clock data, together with direct model-independent high-resolution
astrophysical spectroscopy measurements of $\alpha$ up to redshift $z\sim7$ and
additional model-dependent constraints on $\alpha$ from the cosmic microwave
background and big bang nucleosynthesis, to place stringent (parts per million
level) constraints on the first two terms in the $\alpha$ cosmographic series.
