In this work, we study the ionic effects on the equilibrium size and shape of kinetoplasts, a two-dimensional (2D) network of catenated DNA rings. With increasing ionic strength from 5 to 200 mM, we observe a decrease in kinetoplast size, primarily driven by the long-range electrostatic interactions that give rise to a change in effective DNA width. A fit of the experimentally measured kinetoplast size versus effective width yields a scaling exponent of 0.38. To probe the quantitative effects of ionic strength on kinetoplast size, we develop a scaling argument based on a generalized Flory approach for a 2D polymer represented as monomers on an open lattice. Interestingly, while ionic strength has a significant effect on kinetoplast size, we find that it does not impact the kinetoplast shape.