A magnitude phase-locked loop (MPLL) is a system that synchronizes its output signal in frequency, phase, and magnitude with the dominant sinusoidal component of its input signal. We propose a novel MPLL design based on the model of a synchronverter (i.e., an inverter that behaves towards the power grid like a synchronous generator). The synchronverter model is detached from its usual three-phase power electronics environment, and transformed into a (single phase) MPLL with a wide pull-in range and great noise rejection properties. We prove synchronization under reasonable conditions. Extensive simulation results are provided to validate its performance, and to compare it with existing solutions.