I was wondering how I can calculate the charge of a protein peptide (e.g. "RKTTLVPNTQTASPR") computationally in R or another tool.
A quick google search turns up protcalc, which is able to give a nice pH-dependent table of peptide charges (yours ranges from 3.1 at pH 4 to 1.5 at pH 10). It's on sourceforge, so hopefully the source code (and maybe a publication) is somewhere in there. Granted, this isn't R, but it's not clear from your post how necessary that really is.
BTW, in general "best and most accurate" turns out to be highly subjective (at least the "best" part of that).
Another quick Google search reveals the Peptides R package.
library(Peptides) s <- "RKTTLVPNTQTASPR" charge(s)  2.997683
Optional arguments to
pH (default = 7) and
pKscale (choice of nine, default = "Lehninger"). See
?charge for details.
Another (non-R) option is the EMBOSS suite program iep. I highly recommend installing EMBOSS, it provides a suite of useful command-line tools with output that can be easily read and processed by other sofware, including R.
I've used PropKa in the past to get isoelectric points. Pretty simple to use: