  In this paper, we study the following fractional nonlinear Schr\"odinger
system $$ \left\{% \begin{array}{ll} (-\Delta)^s u +u=\mu_1 |u|^{2p-2}u+\beta
|v|^p|u|^{p-2}u,~~x\in \R^N,\vspace{2mm}\\ (-\Delta)^s v +v=\mu_2
|v|^{2p-2}v+\beta |u|^p|v|^{p-2}v,~~x\in \R^N, \end{array}% \right. $$ where
$0<s<1, \mu_1 >0, \mu_2>0, 1<p<2_s^*/2, 2_s^*=+\infty$ for $N\le 2s$ and
$2_s^*=2N/(N-2s)$ for $N>2s$, and $\beta \in \R$ is a coupling constant. We
investigate the existence and non-degeneracy of proportional positive vector
solutions for the above system in some ranges of $\mu_1,\mu_2, p, \beta$. We
also prove that the least energy vector solutions must be proportional and
unique under some additional assumptions.
