We consider the lagrangian of a self-interacting complex scalar field admitting generically Q-balls solutions. This model is extended by minimal coupling to electromagnetism and to gravity. A stationnary, axially-symmetric ansatz for the different fields is used in order to reduce the classical equations. The system of non-linear partial differential equations obtained becomes a boundary value problem by supplementing a suitable set of boundary conditions. We obtain numerical evidences that the angular excitations of uncharged Q-balls, which exist in flat space-time, get continuously deformed by the Maxwell and the Einstein terms. The electromagnetic and gravitating properties of several solutions, including the spinning Q-balls, are emphasized.
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