We measure the radii and two-dimensional light profiles of a large sample of young, massive star clusters in M83 using archival HST/WFC3 imaging of seven adjacent fields. We use GALFIT to fit the two-dimensional light profiles of the clusters, from which we find effective (half-light) radii, core radii, and slopes of the power-law (EFF) profile ($\eta$). We find lognormal distributions of effective radius and core radius, with medians of $\approx$2.5 pc and $\approx$1.3 pc, respectively. Our results provide strong evidence for a characteristic size of young, massive clusters. The average effective radius and core radius increase somewhat with cluster age. Little to no change in effective radius is observed with increasing galactocentric distance, except perhaps for clusters younger than 100 Myr. We find a shallow correlation between effective radius and mass for the full cluster sample, but a stronger correlation is present for clusters 200-300 Myr in age. Finally, the majority of the clusters are best fit by an EFF model with index $\eta\leq3.0$. There is no strong evidence for change in $\eta$ with cluster age, mass, or galactocentric distance. Our results suggest that clusters emerge from early evolution with similar radii and are not strongly affected by the tidal field of M83. Mass loss due to stellar evolution and/or GMC interactions appear to dominate cluster expansion in the age range we study.