The authors prove the existence of solitary waves with non-vanishing angular momentum for the equation \(\psi _{tt}-\Delta \psi+W'(\psi )=0,\) where \(W\) is a nonnegative potential depending only on \(\left|\psi \right|.\) The proof relies on finding nonnegative cylindrical solutions to a standing equation with suitable integrability properties. The results will be useful to many physical problems.