  We present numerical evidence for the existence of spinning generalizations
for non-topological Q-ball solitons in the theory of a complex scalar field
with a non-renormalizable self-interaction. To the best of our knowledge, this
provides the first explicit example of spinning solitons in 3+1 dimensional
Minkowski space. In addition, we find an infinite discrete family of radial
excitations of non-rotating Q-balls, and construct also spinning Q-balls in 2+1
dimensions.
