language creation

Is it possible to write a programming language with an existing one?  I want to create a game creation program, and have it use it's own language for additional programming.  Something similar to Game Maker.

Yes, but that's not necessarily the best choice.

Usually the best way to do this is to embed an existing scripting language, like LUA, Python, Ruby or Javascript or something.
This is a good choice because you already have a well-established language, with syntax familiar to other developers, and plenty of existing documentation on how to embed it.

But if you insist on your own language or syntax, look into grammars and something like flex/bison.