  We study symplectic geometry of rationally connected $3$-folds. The first
result shows that rationally connectedness is a symplectic deformation
invariant in dimension $3$. If a rationally connected $3$-fold $X$ is Fano or
$b_2(X)=2$, we prove that it is symplectic rationally connected, i.e. there is
a non-zero Gromov-Witten invariant with two insertions being the class of a
point. Finally we prove that many rationally connected $3$-folds are birational
to a symplectic rationally connected variety.
