Yes, and you should do this, abandon FTP instead.
But the main question should be, and how is it done?
Git is a SCM (Source Control Management) tool, that is, a tool for controlling your code, versioning, tagging, history and everything legal that this type of tool can deliver, for legal I mean essential, make use of it, live in danger of losing the code and have nowhere to look after is crazy, not to mention other points. I will not dwell on this, because I could raise a lot of reasons to use it.
But only using SCM does not completely solve your problem of using FTP to deploy. Yes, deploy, you already do this process without knowing the term. It's nothing more than you upload your changes to your server, the moment you did this, you just did a deploy. But this is a very annoying process when manual, is not it? Yes, it's boring and always the same, so there are a lot of tools to do this automated way for you, integration servers keep your changes up for you, and that's great because you will be much faster in your development and will stop of wasting time on repeatable, error prone tasks.
But this is a really great subject, I went over and did not teach with a hands-on, only superficial theory. So I recommend you read about Continuous Integration, and how to implement it. This is sure to change your development process, of course, for much better.