  We prove a restricted projection theorem for Borel subsets of
$\mathbb{Q}_p^n$ in the regime $p>n$. This generalizes results of Gan-Guo-Wang
in the real setting. Our result is effective in the sense that explicit
constants are obtained for various covering numbers. Along the way, we prove a
fully explicit Fourier decoupling theorem for the moment curve in $p$-adic
Cartesian space.
