Context. Sun-like stars shed angular momentum due to the presence of magnetised stellar winds. Magnetohydrodynamic models have been successful in exploring the dependence of this "wind-braking torque" on various stellar properties, however the influence of surface differential rotation is largely unexplored. As the wind-braking torque depends on the rotation rate of the escaping wind, the inclusion of differential rotation should effectively modulate the angular momentum-loss rate based on the latitudinal variation of wind source regions.Aims. Here we aim to quantify the influence of surface differential rotation on the angular momentum-loss rate of the Sun, in comparison to the typical assumption of solid-body rotation. Methods. To do this, we exploit the dependence of the wind-braking torque on the effective rotation rate of the coronal magnetic field, which is known to be vitally important in magnetohydrodynamic models. This quantity is evaluated by tracing field lines through a Potential Field Source Surface (PFSS) model, driven by ADAPT-GONG magnetograms. The surface rotation rates of the open magnetic field lines are then used to construct an open-flux weighted rotation rate, from which the influence on the wind-braking torque can be estimated. Results. During solar minima, the rotation rate of the corona decreases with respect to the typical solid-body rate (the Carrington rotation period is 25.4 days), as the sources of the solar wind are confined towards the slowly-rotating poles. With increasing activity, more solar wind emerges from the Sun's active latitudes which enforces a Carrington-like rotation. Coronal rotation often displays a north-south asymmetry driven by differences in active region emergence rates (and consequently latitudinal connectivity) in each hemisphere.Conclusions. The effect of differential rotation on the Sun's current wind-braking torque is limited. The solar wind-braking torque is ∼ 10 − 15% lower during solar minimum, (compared with the typical solid body rate), and a few percent larger during solar maximum (as some field lines connect to more rapidly rotating equatorial latitudes). For more rapidly-rotating Sun-like stars, differential rotation may play a more significant role, depending on the configuration of the large-scale magnetic field.