Paravascular cerebrospinal fluid (pCSF) surrounding the cerebral arteries within the glymphatic system is pulsatile and moves in synchrony with the pressure waves of the vessel wall. Whether such pulsatile pCSF can infer pulse wave propagation-a property tightly related to arterial stiffness-is unknown and has never been explored. Our recently developed imaging technique, dynamic diffusion-weighted imaging (dynDWI), captures the pulsatile pCSF dynamics in vivo and can explore this question. In this work, we evaluated the time shifts between pCSF waves and finger pulse waves, where pCSF waves were measured by dynDWI and finger pulse waves were measured by the scanner's built-in finger pulse oximeter. We hypothesized that the time shifts reflect brain-finger pulse wave travel time and are sensitive to arterial stiffness. We applied the framework to 36 participants aged 18-82 years to study the age effect of travel time, as well as its associations with cognitive function within the older participants (N =15, age > 60 years). Our results revealed a strong and consistent correlation between pCSF pulse and finger pulse (mean CorrCoeff = 0.66), supporting arterial pulsation as a major driver for pCSF dynamics. The time delay between pCSF and finger pulses (TimeDelay) was significantly lower (i.e., faster pulse propagation) with advanced age (Pearson's r = -0.44, p = 0.007). Shorter TimeDelay was further associated with worse cognitive function in the older participants. Overall, our study demonstrated pCSF as a viable pathway for measuring intracranial pulses and encouraged future studies to investigate its relevance with cerebrovascular functions.