  We define a torus action on the (complex) Cayley Grassmannian $X$. Using this
action, we prove that $X$ is a singular variety. We also show that the singular
locus is smooth and has the same cohomology ring as that of $\mathbb{CP}^5$.
Furthermore, we identify the singular locus with a quotient of $G_2^\mathbb{C}$
by a parabolic subgroup.
