In the context of a special class of tensor-multi-scalar theories of gravity for which the target-space metric admits as a Killing field a generator of a one-parameter group of point transformations under which the theory is invariant, we present rotating vacuum solutions, namely with no matter fields. These objects behave like nontopological solitons, whose primary stability is due to the conserved charge arising from the global symmetry. We consider theories with two and three scalar fields, different Gauss curvatures and quartic interaction coefficients. As it occurs for boson stars, their angular momentum is quantized. Ergoregions appear for compact enough solutions in the two scalars theory but are absent in the three scalars case for the two first nonzero winding numbers.