  We use lattice QCD and the L\"uscher method to study elastic pion-nucleon
scattering in the isospin $I = 3/2$ channel, which couples to the
$\Delta(1232)$ resonance. Our $N_f=2+1$ flavor lattice setup features a pion
mass of $m_\pi \approx 250$ MeV, such that the strong decay channel $\Delta
\rightarrow \pi N$ is close to the threshold. We present our method for
constructing the required lattice correlation functions from single- and
two-hadron interpolating fields and their projection to irreducible
representations of the relevant symmetry group of the lattice. We show
preliminary results for the energy spectra in selected moving frames and
irreducible representations, and extract the scattering phase shifts. Using a
Breit-Wigner fit, we also determine the resonance mass $m_\Delta$ and the
$g_{\Delta-\pi N}$ coupling.
