It has long been accepted that a possible mechanism for explaining the existence of magnetic white dwarfs is the merger of two white dwarfs, as there are viable mechanisms for producing sustainable magnetic fields within the merger product. However, the lack of rapid rotators in the magnetic white dwarf population has always been considered a problematic issue of this scenario. Smoothed particle hydrodynamics simulations show that in mergers in which the two white dwarfs have different masses, a disc around the central compact object is formed. If the central object is magnetized, it can interact with the disc through its magnetosphere. The torque applied by the disc changes the spin of the star, whereas the transferred angular momentum from the star to the disc determines the properties of the disc. In this work, we build a model for the disc evolution under the effect of magnetic accretion, and for the angular momentum evolution of the star, which can be compared with the observations. Our model predicts that the magnetospheric interaction of magnetic white dwarfs with their discs results in a significant spin-down, and we show that for magnetic white dwarfs with relatively strong fields (larger than 10 MG) the observed rotation periods of the magnetic white dwarf population can be reproduced. We also investigate whether turbulence can be sustained during the late phases of the evolution of the system. When a critical temperature below which turbulence is not sustained is introduced into the model, the periods of the three fast rotating, strongly magnetic, massive white dwarfs in the solar neighbourhood are recovered.