Hi I have two computers, one at work and one at home. The computer at work is doing some calculations and always outputs to a textfile. It's on 24 hours. So I was wondering if I can write a program that uploads the file to an ftp every night at a specific time so I can access it at home
Yes you can. You should become familiar with the FTP protocol before you attempt this. However, I'd imagine if you did a google search you could find software that is already available to do this.
If you are not a developer, then a language like VB.NET would be an easier way to accomplish this without having to learn a language like C++.