  The migration of low-mass planets is driven by the differential Lindblad
torque and the corotation torque in non-magnetic viscous models of
protoplanetary discs. The corotation torque has recently received detailed
attention as it may slow down, stall, or reverse migration. In laminar viscous
disc models, the long-term evolution of the corotation torque is intimately
related to viscous and thermal diffusion processes in the planet's horseshoe
region. This paper examines the properties of the corotation torque in discs
where MHD turbulence develops as a result of the magnetorotational instability,
considering a weak initial toroidal magnetic field. We present results of 3D
MHD simulations carried out with two different codes. Non-ideal MHD effects and
the disc's vertical stratification are neglected, and locally isothermal disc
models are considered. The running time-averaged torque exerted by the disc on
a fixed planet is evaluated in three disc models. We first present results with
an inner disc cavity (planet trap). As in viscous disc models, the planet is
found to experience a positive running time-averaged torque over several
hundred orbits, which highlights the existence of an unsaturated corotation
torque maintained in the long term in MHD turbulent discs. Two disc models with
initial power-law density and temperature profiles are also adopted, in which
the time-averaged torque is found to be in decent agreement with its
counterpart in laminar viscous disc models with similar viscosity at the planet
location. Detailed analysis of the averaged torque density distributions
indicates that the differential Lindblad torque takes very similar values in
MHD turbulent and laminar viscous discs, and there exists an unsaturated
corotation torque in MHD turbulent discs. This analysis also reveals the
existence of an additional corotation torque in weakly magnetized discs.
