Can I upload journal articles to a private git repo?
I store all important papers in a cloud, where I am the only one (beside the operating people) that has access. There are several such cloud solutions around, such as from DropBox, Microsoft and many others.
Unless there is an explicit statement that does not allow this, it is perfect (and until now, there has not been such a statement). The key is that you restrict access to yourself.
I would not use git for your case; it is intended for software development.