It is an interesting matter to have a facebook application built by own. There is enough restriction to use HTML code or using JS in that app. But adding this app in iframe mode you can place any kind of application you have made. You Application must be in your own hosting server. Facebook will just redirect to this location within there view.
To get started just go to the Developers link in your facebook account and you will get futher instruction.
My Application:
Name: Recent Event in RUET
To add this Application on your Facebook Profile :Get This: Click Here

