The segregating sites in parsimony are formally called steps. Any number of programs will do this but I don't really use R, particularly for phylogeny, You can of course simply look at the raw treefile, all the data is there (described in the last paragraph). If look at the options for genetic distance, in parsimony this will be an integer and again the technical name is steps and is the segreating sites you want.
ETE3 package will work (but you'd need to pipe it through Biopython), as well as specific standalone packages
Figtree, the steps or 'genetic distance' on the branches on the branches option is in the check box. The heavy weight program for tracking step associated phylogeny using parsimony is
Mesquite and its famous grandparent is called
I suspect its a nomenclature thing, the options probably talk about genetic distance because few people do parsimony phylogeny now. Thats the option you want and you will know because it will be >>1, whilst distance and model-based methods will be between 0 to 1. From a tree viewing it doesn't matter if the genetic distance is 0 to 1 or 1 and beyond because its all proportional. Its just an option thing you are missing. Thus if there is an option, e.g. to include bootstrap support on the tree, there'll be an option for genetic distance.
Just make sure you don't confuse the number of steps per branch with a consensus statistic, because there're completely different but might give similar looking outputs. Again its easily checked against the raw treefile because the "steps" will be immediately adajacent to the taxa name for the "twigs" (terminal branches) in the tree.