This paper proposes a novel fractional proportional-resonant controller, which applies fractional order calculus to the well-known proportional-resonant controllers. The focus of the study is the current control loop of voltage source converters. The main merit of the proposed fractional controller formulation lies into the use of fractional exponents in the integro-derivative parts obtaining a controller with an extra degree of freedom. This degree of freedom allows the phase delay to be improved for a wide frequency range in comparison with the conventional proportional-resonant controllers. Furthermore, the obtained controller results in a lower order transfer function that reduces the computational burden when multiple current frequencies have to be tracked. As fractional integro-derivative exponents are not directly implementable, five mathematical approaches are explored, selecting the Chareff’s approximation for the fractional controller operator’s implementation. A tuning procedure for such a controller is also addressed. The new controller formulation is validated in a 20 kVA laboratory set-up based on a silicon-carbide converter, and it is implemented in a DSP. Two AC output converter’s configurations are considered to demonstrate the controllers’ tracking capability; short-circuited (balanced fault) output, and grid-connected operation. This last case is evaluated operating as active filter and delivering fundamental component to a non-ideal grid.