Intracranial arterial stiffening is a potential early marker of emerging cerebrovascular dysfunction and could be mechanistically involved in disease processes detrimental to brain function via several pathways. A prominent consequence of arterial wall stiffening is the increased velocity at which the systolic pressure pulse wave propagates through the vasculature. Previous non-invasive measurements of the pulse wave propagation have been performed on the aorta or extracranial arteries with results linking increased pulse wave velocity to brain pathology. However, there is a lack of intracranial "target-organ" measurements. Here we present a 4D flow MRI method to estimate pulse wave velocity in the intracranial vascular tree. The method utilizes the full detectable branching structure of the cerebral vascular tree in an optimization framework that exploits small temporal shifts that exists between waveforms sampled at varying depths in the vasculature. The method is shown to be stable in an internal consistency test, and of sufficient sensitivity to robustly detect age-related increases in intracranial pulse wave velocity.