  We consider the $U(1)$ gauged two-component Friedberg-Lee-Sirlin model in 3+1
dimensional Minkowski spacetime, which supports non-topological soliton
configurations. Here we found families of axially-symmetric spinning gauged
Q-balls, which possess both electric and magnetic fields. The coupling to the
gauge sector gives rise to a new branch of solutions, which represent the
soliton configuration coupled to a circular magnetic flux. Further, in
superconducting phase this branch is linked to vorton type solutions which
represent a vortex encircling the soliton. We discuss properties of these
solutions and investigate their domains of existence.
