Experiment with creating a script file on Windows (e.g., .bat) that calls "bash -c git" while passing all arguments and then point RStudio to this script. Also, pay attention to the location where the RSA key is stored (it may have to be stored both on Linux and on Windows).
If this does not work, then "in for a penny, in for a pound" (although Windows is the pound and git is the penny). I would install git on Windows (git and git bash for Windows work well) and, if really really needed, set up a sync of the git config file between Linux and Windows. In my view, it gets the job done without jumping through too many hoops.