  Quasar absorption spectral data indicate the presence of a spatial gradient
in the electromagnetic fine-structure constant $\alpha$ on cosmological length
scales. We point out that experiments with accelerometers, including torsion
pendula and atom interferometers, can be used as sensitive probes of
cosmological spatial gradients in the fundamental constants of nature, which
give rise to equivalence-principle-violating forces on test masses. Using
laboratory data from the E\"ot-Wash experiment, we constrain spatial gradients
in $\alpha$ along any direction to be $| \boldsymbol{\nabla} \alpha / \alpha |
< 6.6 \times 10^{-4}~(\textrm{Glyr})^{-1}$ at $95\%$ confidence level. Our
result represents an order of magnitude improvement over laboratory bounds from
clock-based searches for a spatial gradient in $\alpha$ directed along the
observed cosmological $\alpha$-dipole axis. Improvements to accelerometer
experiments in the foreseeable future are expected to provide sufficient
sensitivity to test the cosmological $\alpha$-dipole seen in astrophysical
data.
