We present measurements of the polarization of X-rays in the 2-8 keV band from the nucleus of the radio galaxy Centaurus A (Cen A), using a 100 ks 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% confidence (MDP99) of 6.5% using a weighted, spectral model-independent calculation in the 2-8 keV band. The polarization angle ψ is consequently unconstrained. Spectral fitting across three orders of magnitude in X-ray energy (0.3-400 keV) demonstrates that the SED of Cen A is well described by a simple power law with moderate intrinsic absorption (NH ∼1023 cm-2) and a Fe Kα emission line, although a second unabsorbed power law is required to account for the observed spectrum at energies below 2 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 the 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 Kα emission line support a picture where electrons are accelerated in a region of highly disordered magnetic fields surrounding the innermost jet.