  We report a comprehensive muon spin rotation ($\mu$SR) study of the
prototypical magnetoelectric antiferromagnet Cr$_2$O$_3$. We find the
positively charged muon ($\mu^+$) occupies several distinct interstitial sites,
and displays a rich dynamic behavior involving local hopping, thermally
activated site transitions and the formation of a charge-neutral complex
composed of a muon and an electron polaron. The discovery of such a complex has
implications for the interpretation of $\mu$SR spectra in a wide range of
magnetic oxides, and opens a route to study the dopant characteristics of
interstitial hydrogen impurities in such materials. We address implications
arising from implanting a $\mu^+$ into a linear magnetoelectric, and discuss
the challenges of observing a local magnetoelectric effect generated by the
charge of the muon.
