I am a student working on a implementation of a signup system in Python. In order to allow you to signup, the programme will edit a .csv file (with the Username and Password as columns). In order to allow the use of that programme I need something like a server, which stores the master file and when a user runs the programme it updates the file. I thought of using git for that (as I lack the resources for a server), would that be a viable option and how would I allow the editing of that file without the need of having github account
Git is designed as a version control system.  It's designed to store and version files, especially text files, in a way such that they are easily retrievable and have a useful version history.
What you are looking for is a database backend or a server hosting platform.  Git is not good for that, since it keeps a history of every file, which you do not need, and which will eventually lead to your repository growing very large.  Git also will not perform especially well in this situation, compared to virtually any database engine in existence.
Furthermore, if, despite this advice, you do use one of the major Git hosting platforms for this, they will probably eventually ask you to leave, as making a large number of automated, programmatic commits of data files to a repository causes various problems for hosting repositories, the least of which is the bloat and repacking, since this leads to pathological performance when packing.
If you want a reasonably cheap hosting platform, there are many shared web hosting providers around that are just a few dollars a month.  However, be aware that if you are dealing with transferring people's money, there are a variety of legal regulations with which you must comply based on the jurisdiction, and you will definitely want to consult an attorney before starting.  If you can't afford a server, you probably can't afford to do this legally.  Further discussion of this is probably off topic, though.
Using Git as a something like a server