  We deal with the virtual element method (VEM) for solving the Poisson
equation on a domain $\Omega$ with curved boundaries. Given a polygonal
approximation $\Omega_h$ of the domain $\Omega$, the standard order $m$ VEM
[6], for $m$ increasing, leads to a suboptimal convergence rate. We adapt the
approach of [16] to VEM and we prove that an optimal convergence rate can be
achieved by using a suitable correction depending on high order normal
derivatives of the discrete solution at the boundary edges of $\Omega_h$,
which, to retain computability, is evaluated after applying the projector
$\Pi^\nabla$ onto the space of polynomials. Numerical experiments confirm the
theory.
