Nontopological solitons with nonzero vorticities are considered in the theory of a complex scalar field with renormalizable self-interactions in (2+1)-dimensional spacetime. These nontopological vortices are characterized by the fact that they carry a nonzero angular momentum in addition to the global Abelian charge. The existence of such objects is shown in rotationally symmetric cases. Such rotationally symmetric configurations are ring shaped around the center. Their stability against decay into mesons is demonstrated analytically.