In inertial microfluidics lift forces cause a particle to migrate across streamlines to specific positions in the cross section of a microchannel. We control the rotational motion of a particle and demonstrate that this allows to manipulate the lift-force profile and thereby the particle's equilibrium positions. We perform two-dimensional simulation studies using the method of multi-particle collision dynamics. Particles with unconstrained rotational motion occupy stable equilibrium positions in both halfs of the channel while the center is unstable. When an external torque is applied to the particle, two equilibrium positions annihilate by passing a saddle-node bifurcation and only one stable fixpoint remains so that all particles move to one side of the channel. In contrast, non-rotating particles accumulate in the center and are pushed into one half of the channel when the angular velocity is fixed to a non-zero value.