  We define cluster $R$-matrices as sequences of mutations in triangular grid
quivers on a cylinder, and show that the affine geometric $R$-matrix of
symmetric power representations for the quantum affine algebra
$U_q^\prime(\hat{\mathfrak{sl}}_n)$ can be obtained from our cluster
$R$-matrix. A quantization of the affine geometric $R$-matrix is defined,
compatible with the cluster structure. We construct invariants of the quantum
affine geometric $R$-matrix as quantum loop symmetric functions.
