RStudio is why you're here
. At its simplest, it's a front end for R (What is R?). In addition to a console for the R language/environment, it has a text editor, a file explorer (similar to your operating system file manager), and other bells and whistles. One of those added features is the ability to see what you have in Git and manage files (by committing/pushing/pulling/"diff"ing). So if you have Git in sync where you're using RStudio (e.g., your laptop), you will see the same things JIRA would see, in terms of file history, branching, commit messages, etc. You can add your R work (.R/.Rmd working code files, .Rdata data objects (including your session state), .Rhistory, plot files, etc.) to Git.
I've only recently started using Git with RStudio (as opposed to through the command line), but you can see how to do that here: Version Control with Git and SVN. There are a ton of links in that help article with how and why you'd want to do that. If you are already a user of Git, it's extremely simple to view and manage your repository through RStudio.