Yes just visit the oracle website and then click the download menu button. And then you have now your oracle installer. I hope you will..
I would suggest you use MySQL instead, if you can. Not that it's better, necessarily, but rather because there is much more documentation on it.
Note that the free download version is only licensed "for the purpose of developing, testing, prototyping and demonstrating your application, and not for any other purpose. If you use the application you develop under this license for any internal data processing or for any commercial or production purposes, or you want to use the programs for any purpose other than as permitted under this agreement, you must obtain a production release version of the program by contacting us or an Oracle reseller to obtain the appropriate license."