It certainly is possible, but it sounds like EC2 is not the best option for you. For examples of people doing it, google for "django ec2" and check out the
first and second links. links like this or this (edited because this question is now the top google result for that query!)
In a very oversimplified sense, EC2 is just a server you can rent by the hour. You can have it run windows or linux, and then install python and django like you normally would. In fact there is probably an image that has django preconfigured already. What stage of your project are you at? Just researching, or have you gotten stuck on a particular problem with either django or ec2?
Ok, I think what you are confused about is that there are all different types of hosting out there. At one extreme, you can pay for your very own physical server, install your own operating system (like windows or linux), install your own python, you own web server like apache or IIS, your own django libraries, your own database (like mysql) etc, and then upload your web site to that. At the other extreme you can pay for an account on a shared hosting service, where someone else has done all the setup of the OS, the python, the web server, etc, and all you need to do is upload your web site code. EC2 is a lot closer to the first extreme, and is probably overkill for you. I think in your case you should be looking for a more managed solution.
I would check out this web page, which lists a bunch of different django hosting companies: Django hosting
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