I do not have face time application on my iPhone 4

In whay country was this purchased in? Some countries, such as Saudi Arabia, UAE, ban FaceTime. If the phone was purchased in such a country, it cannot be added.

Otherwise, here is another suggestion: First, go to Settings, then General, then Restrictions, and verify that FaceTime was not turned off.

Hopefully, you are also aware that the iPhone does not have a dedicated FaceTime application, but rather, it is accessed through the Contacts app after selecting a contact.

Facetime is not an app. It's accessed through Contacts.