Yes you can.
Especially you recognize any of these in you:
– You have a dream of creating your own game (good, good – every goal begins with a vision)
– You might have tried to develop some games (even a better sign)
– You are interested in games (chances are that you enjoy games, and can build a career around them)
– You are jealous to successful game developers, or feel at least little bit jealous sometimes when you see success (this is a good sign, we humans are jealous to something what we want)
– You have developed a game demo (a very, very good sign – this means you got what it takes to developer games!)
– You are interested in both programming and business of game development (being a producer means you have to take responsibility not only about programming)
Sounded familiar to you?