Finite radius electron‐beam transport in a linear wiggler free‐electron laser with a guide magnetic field is investigated. The addition of a guide magnetic field improves the beam confinement, but also leads to a detrimental drift in the direction transverse to the wiggler magnetic field. The introduction of a rotational transformation of the wiggler magnetic field is proposed to further improve the beam confinement. It is shown that the transformation results in a stable, uniform, solid body rotation of the beam provided (a) the guide field is larger than the amplitude of the wiggler field, (b) the electron drift velocity is much smaller than the rotation speed of the wiggler field as seen by the beam, and (c) the wiggler field rotates in the direction opposite to the direction of the electron gyromotion in the guide field. Theoretical predictions of the improvement of the radial beam transport with the introduction of the rotation of the wiggler field are confirmed in numerical simulations.