We use a new spherical accretion recipe tested on N-body simulations to measure the observed mass accretion rate (MAR) of 129 clusters in the Cluster Infall Regions in the Sloan Digital Sky Survey (CIRS) and in the Hectospec Cluster Survey (HeCS). The observed clusters cover the redshift range of 0.01 14 - 1015 h-1 M⊙. Based on three-dimensional mass profiles of simulated clusters reaching beyond the virial radius, our recipe returns MARs that agree with MARs based on merger trees. We adopt this recipe to estimate the MAR of real clusters based on measurements of the mass profile out to ∼3R200. We use the caustic method to measure the mass profiles to these large radii. We demonstrate the validity of our estimates by applying the same approach to a set of mock redshift surveys of a sample of 2000 simulated clusters with a median mass of M200 = 1014 h-1 M⊙ as well as a sample of 50 simulated clusters with a median mass of M200 = 1015 h-1 M⊙: the median MARs based on the caustic mass profiles of the simulated clusters are unbiased and agree within 19% with the median MARs based on the real mass profile of the clusters. The MAR of the CIRS and HeCS clusters increases with the mass and the redshift of the accreting cluster, which is in excellent agreement with the growth of clusters in the ΛCDM model.