  We consider a Weyl-Lorentz-$U(1)$-invariant gravity model written in terms of
a scalar field, electromagnetic field and nonmetricity without torsion and
curvature, the so-called symmetric teleparallel geometry, in three dimensions.
Firstly, we obtain variational field equations from a Lagrangian. Then, we find
some classes of circularly symmetric rotating solutions by making only a metric
ansatz. The coincident gauge of symmetric teleparallel spacetime allows us for
doing so.
