The main purpose of this paper is to obtain some regularity results to the following discontinuous quasilinear divergence form elliptic equation \[ \begin{cases}\mathrm{div}(a^{ij}(x, u)D_ju+a^{i}(x, u))+ a(x, u, Du)=0&\text{in }\Omega,\\ u=0 &\text{on }\partial\Omega, \end{cases}\tag{P} \] where \(\Omega \) is a bounded domain of \(\mathbb R^n, n\geq 2.\) The discontinuous nonlinear terms \(a^{ij},\; a^i: \Omega \times \mathbb R \rightarrow \mathbb R \) and \(a: \Omega \times \mathbb R \times \mathbb R^n \rightarrow \mathbb R\) are Carathéodory functions that satisfy some controlled growth conditions and the non-smooth boundary \(\partial\Omega\) is supposed to be well approximated by hyperplanes at each point and at each scale (Reifenberg flat). Further, the authors prove that the gradient \(Du\) belongs to an appropriate Morrey space. Also global Hölder continuity of the weak solution \(u\) with exact value of the corresponding exponent is established.