Yes, and you should do that, abandon FTP once and for all.
But the main question must be, and how do you do it?
Git is a SCM (Source Control Management) tool, which is a tool for controlling your code, versioning, tag, history, and everything that this kind of tool can deliver, by legal I mean essential, make use of it, live with the danger of losing the code and have no place to look for afterwards is crazy, not to mention other points. I will not delve into this, because it could raise numerous reasons to use it.
But just using SCM doesn’t completely solve your FTP problem to deploy. Yes, deploy, you already do this process without knowing the term. It’s nothing but you upload your changes to your server, at the time you did this, you just deploy. But this is a very boring process when manual, isn’t it? Yes, it’s boring and always the same, so there are many tools to do this in an automated way for you, continuous integration servers that raise your changes to you, and that’s great because you’ll be much faster in your development and will stop wasting time on repeatable and error-prone tasks.
But this is a really big subject, I passed well over and did not teach with a hands-on, only superficial theory. That’s why I recommend you read about Continuing Integration, and how to implement it. This will surely change your development process, of course, for much better.
Tip: if you understand English, I strongly recommend you in this GIT course: https://www.codeschool.com/courses/try-git and while deploy is very complicated, it all depends on the project, I started with Capistrano which is great for Ruby on Rails.
– Adriano Resende