We consider magnetic Weyl metals as a platform to achieve current control of magnetization textures with transport currents utilizing their underlying band geometry. We show that the transport current in a Weyl semimetal produces an axial magnetization due to orbital magnetic moments of the Weyl electrons. The associated axial magnetization can generate a torque acting on the localized magnetic moments. For the case of a magnetic vortex in a nanodisk of Weyl materials, this current-induced torque can be used to reverse its circulation and polarity. We discuss the axial magnetization torques in Weyl metals on general symmetry grounds and compare their strength to current-induced torques in more conventional materials.