Context. Planetary migration is a key link between planet formation models and observed exoplanet statistics. So far, the theory of planetary migration has focused on the interaction of one or more planets with an inviscid or viscously evolving gaseous disk. Turbulent viscosity is thought to be the main driver of the secular evolution of the disk, and it is known to affect the migration process for intermediate- to high-mass planets. Recently, however, the topic of wind-driven accretion has experienced a renaissance because evidence is mounting that protoplanetary disks may be less turbulent than previously thought, and 3D non-ideal magnetohydrodynamic modeling of the wind-launching process is maturing. Aims. We investigate how wind-driven accretion may affect planetary migration. We aim for a qualitative exploration of the main effects and not for a quantitative prediction. Methods. We performed 2D hydrodynamic planet-disk interaction simulations with the FARGO3D code in the (r, ϕ) plane. The vertical coordinate in the disk and the launching of the wind are not treated explicitly. Instead, the torque caused by the wind onto the disk is treated using a simple two-parameter formula. The parameters are the wind mass-loss rate and the lever arm. Results. We find that the wind-driven accretion process replenishes the co-orbital region in a different way than the viscous accretion process. The former always injects mass from the outer edge of the co-orbital region, and always removes mass from the inner edge, while the latter injects or removes mass from the co-orbital region depending on the radial density gradients in the disk. As a consequence, the migration behavior can differ strongly, and can under certain conditions drive rapid type-III-like outward migration. We derive an analytic expression for the parameters under which this outward migration occurs. Conclusions. If wind-driven accretion plays a role in the secular evolution of protoplanetary disks, planetary migration studies have to include this process as well because it can strongly affect the resulting migration rate and migration direction.