  For a Kac-Moody group $G$, double Bruhat cells $G^{u,e}$ ($u$ is a Weyl group
element) have positive geometric crystal structures. In arXiv:1210.2533, it is
shown that there exist birational maps between `cluster tori'
$\mathcal{X}_{\Sigma}$ (resp. $\mathcal{A}_{\Sigma}$) and $G_{\rm Ad}^{u,e}$
(resp. $G^{u,e}$), and they are extended to regular maps from cluster
$\mathcal{X}$ (resp. $\mathcal{A}$) -varieties to $G_{\rm Ad}^{u,e}$ (resp.
$G^{u,e}$). The aim of this article is to construct certain positive geometric
crystal structures on the cluster tori $\mathcal{X}_{\Sigma}$ and
$\mathcal{A}_{\Sigma}$ by presenting their explicit formulae. In particular,
the geometric crystal structures on the tori $\mathcal{A}_{\Sigma}$ are
obtained by applying the twist map. As a corollary, we see the sets of
$\mathbb{Z}^T$-valued points of the cluster varieties have plural structures of
crystals.
