Summary: In this work we prove that the initial value problem associated to the fractional two-dimensional Benjamin-Ono equation \[\begin{aligned} u_t+ D^\alpha_x u_x+\mathcal{H} u_{yy} & =0,\qquad (x,y)\in\mathcal{R}^2,\ t\in\mathcal{R},\\ u(x,y,0) &= u_0(x, y),\end{aligned}\] where \(0<\alpha\le 1\), \(D^\alpha_x\) denotes the operator defined through the Fourier transform by \[(D^\alpha_x f)\widehat{}(\xi,\eta):= |\xi|^\alpha\widehat f(\xi,\eta),\] and \(\mathcal{H}\) denotes the Hilbert transform with respect to the variable \(x\), is locally well-posed in the Sobolev space \(H^*(\mathbb{R}^2)\) with \(s>\frac{3}{2}+ \frac{1}{4}\ (1-\alpha)\).