  This paper is devoted to study the existence and multiplicity solutions for
the nonlinear
  Schr\"odinger-Poisson systems involving fractional Laplacian operator:
\begin{equation}\label{eq*}
  \left\{ \aligned
  &(-\Delta)^{s} u+V(x)u+ \phi u=f(x,u), \quad &\text{in }\mathbb{R}^3,
  &(-\Delta)^{t} \phi=u^2, \quad &\text{in }\mathbb{R}^3,
  \endaligned
  \right. \end{equation} where $(-\Delta)^{\alpha}$ stands for the fractional
Laplacian of order $\alpha\in (0\,,\,1)$. Under certain assumptions on $V$ and
$f$, we obtain infinitely many high energy solutions for \eqref{eq*} without
assuming the Ambrosetti-Rabinowitz condition by using the fountain theorem.
