  In this paper, we study the following fractional Choquard system
\begin{align*}
  \begin{split}
  \left\{
  \begin{array}{ll}
  (-\Delta)^{1/2}u=\lambda_1 u+(I_\mu*F(u,v))F_u (u,v),
  \quad\mbox{in}\ \ \mathbb{R},
  (-\Delta)^{1/2}v=\lambda_2 v+(I_\mu*F(u,v)) F_v(u,v),
  \quad\mbox{in}\ \ \mathbb{R},
  \displaystyle\int_{\mathbb{R}}|u|^2\mathrm{d}x=a^2,\quad
\displaystyle\int_{\mathbb{R}}|v|^2\mathrm{d}x=b^2,\quad u,v\in
H^{1/2}(\mathbb{R}),
  \end{array}
  \right.
  \end{split}
  \end{align*} where $(-\Delta)^{1/2}$ denotes the $1/2$-Laplacian operator,
$a,b>0$ are prescribed, $\lambda_1,\lambda_2\in \mathbb{R}$,
$I_\mu(x)=\frac{{1}}{{|x|^\mu}}$ with $\mu\in(0,1)$, $F_u,F_v$ are partial
derivatives of $F$ and $F_u,F_v$ have exponential critical growth in
$\mathbb{R}$. By using a minimax principle and analyzing the monotonicity of
the ground state energy with respect to the prescribed masses, we obtain at
least one normalized ground state solution for the above system.
