  We present measurements of the polarization of X-rays in the $2-8 \thinspace
\mathrm{keV}$ band from the nucleus of the radio galaxy Centaurus A (Cen A),
using a 100ks observation from the Imaging X-ray Polarimetry Explorer (IXPE).
Nearly simultaneous observations of Cen A were also taken with the Swift,
NuSTAR, and INTEGRAL observatories. No statistically significant degree of
polarization is detected with IXPE. These observations have a minimum
detectable polarization at $99 \%$ percent confidence (MDP$_{99}$) of $6.5 \%$
using a weighted, spectral model-independent calculation in the $2-8 \thinspace
\mathrm{keV}$ band. The polarization angle $\psi$ is consequently
unconstrained. Spectral fitting across three orders of magnitude in X-ray
energy ($0.3-400 \thinspace \mathrm{keV}$) demonstrates that the SED of Cen A
is well described by a simple power law with moderate intrinsic absorption
($N_H \sim 10^{23} \thinspace \mathrm{cm}^{-2}$) and a Fe K$\alpha$ emission
line, although a second unabsorbed power law is required to account for the
observed spectrum at energies below $2 \thinspace \mathrm{keV}$. This spectrum
suggests that the reprocessing material responsible for this emission line is
optically thin and distant from the central black hole. Our upper limits on the
X-ray polarization are consistent with the predictions of Compton scattering,
although the specific seed photon population responsible for production of the
X-rays cannot be identified. The low polarization degree, variability in the
core emission, and the relative lack of variability in the Fe K$\alpha$
emission line support a picture where electrons are accelerated in a region of
highly disordered magnetic fields surrounding the innermost jet.
