  If there is a substantial cosmological radio background, there should be a
radio Sunyaev-Zeldovich (SZ) effect that goes along with it. The radio
background Comptonization leads to a slight photon excess at all wavelengths,
while Comptonization of the CMB at low frequencies leads to a decrement. For
levels of the radio background consistent with observations, these effects
cancel each other around $\nu\simeq 735~$MHz, with an excess at lower
frequencies and a decrement at higher frequencies. Assuming a purely
cosmological origin of the observed ARCADE radio excess, at $\nu \lesssim
20\,{\rm GHz}$ the signal scales as $\Delta T / T_{\rm CMB}\simeq 2\,y\left[
(\nu/735\,{\rm MHz})^{-2.59}-1\right]$ with frequency and the Compton-$y$
parameter of the cluster. For a typical cluster, the total radio SZ signal is
at the level of $\Delta T\simeq 1\,{\rm mK}$ around the null, with a steep
scaling towards radio frequencies. This is above current raw sensitivity limits
for many radio facilities at these wavelengths, providing a unique way to
confirm the cosmological origin of the ARCADE excess and probe its properties
(e.g., redshift dependence and isotropy). We also give an expression to compute
the radio-analogue of the kinematic SZ effect, highlighting that this might
provide a new tool to probe large-scale velocity fields and the cosmic
evolution of the radio background.

Cosmology and Nongalactic Astrophysics