  The tetragonal heavy-fermion superconductor CeRh$_2$As$_2$ ($T_{\rm c}=0.3$
K) exhibits an exceptionally high critical field of 14 T for $\textbf{B}
\parallel \textbf{c}$. It undergoes a field-driven first-order phase transition
between superconducting (SC) states, potentially transitioning from
spin-singlet to spin-triplet superconductivity. To elucidate the underlying
pairing mechanism, we probe spin fluctuations in CeRh$_2$As$_2$ using neutron
scattering. We find dynamic $(\pi,\pi)$ antiferromagnetic spin correlations
with an anisotropic quasi-two-dimensional correlation volume. Our data place an
upper limit of 0.31 $\mu_{\rm B}$ on the staggered magnetization of
corresponding N\'{e}el orders at $T=0.08$ K. Density functional theory (DFT)
calculations, treating Ce $4f$ electrons as core states, show that the AFM wave
vector connects significant areas of the Fermi surface. Our findings show the
dominant excitations in CeRh$_2$As$_2$ for $\hbar\omega< 1.2$~meV are magnetic
and indicate superconductivity in CeRh$_2$As$_2$ is mediated by AFM spin
fluctuations associated with a proximate quantum critical point.
