You can run custom commands in Texmaker (
User -> User Commands) as well as TeXstudio (
Configure -> Build -> User Commands). With that it should be possible to call Git command line tools from within the editor. Moreover in TeXstudio, you can combine this with scripting and triggers, which allows you to automatically trigger these actions e.g. on file save.
If you tell me which git commands you need, I could provide example code.
Below is an example for TeXstudio, in which the commands are called via scripting. Create the scripts at
User Macros -> Edit Macros.... Since I'm not into git, I don't know if the actual git calls are correct, however it should illustrate the idea.
A simple plain call to an external program. On first execution of the script TXS will ask you if you trust the script to execute external programs.
This a bit more fancy. First, the script asks the user for a commit comment. Second, the trigger
?save-file means that the script is called everytime you save a file.
Of course, you can further extend the scripts according to your needs.