  A $k$-uniform tight cycle is a $k$-graph with a cyclic ordering of its
vertices such that its edges are precisely the sets of $k$ consecutive vertices
in that ordering. A $k$-uniform tight path is a $k$-graph obtained by deleting
a vertex from a $k$-uniform tight cycle. We prove that the Ramsey number for
the $4$-uniform tight cycle on $4n$ vertices is $(5 +o(1))n$. This is
asymptotically tight. This result also implies that the Ramsey number for the
$4$-uniform tight path on $n$ vertices is $(5/4 + o(1))n$.
