Abstract The supercurrent diode effect (SDE) describes superconducting systems where the magnitude of the superconducting-to-normal state switching current differs for positive and negative current bias. Despite the ubiquity of such diode effects in Josephson devices, the fundamental conditions to observe a diode effect in a Josephson junction and achieve perfect diode efficiency remain unclear. In this work, we theoretically analyze the supercurrent diode properties of a chiral nanotube-based weak link. We show a perfect diode effect and anomalous phase can develop across the junction when a magnetic field is applied parallel to the tube despite the absence of spin-orbit interactions in the system. We show the SDE in the junction is independent of the anomalous phase. We determine a persistent current along the nanotube associated with the Little-Parks effect can activate SDE, even in the absence of higher-order pair tunneling processes. We show this type of SDE can lead to, in principle, a perfect diode efficiency, highlighting how persistent currents can be used to engineer high efficiency supercurrent diodes.