Can a developer make an app that can be controlled with Siri? [duplicate]

As of now, there is no API for Apple developers to use to connect to Siri. That may or may not be changed in the future; see e.g. http://daringfireball.net/2011/10/iphone_4s for discussion.

As Victor mentioned, there is currently no API which allows an app to be accessed using the Siri interface. However, the speech-to-text portion of Siri is available automatically. Any app which displays the standard keyboard will have a microphone icon which allows you to speak, and Siri will transcribe that to fill in the field for you. You won't be able to access it by holding the home button, but you won't have to type it in either. See the bottom of Apple's Siri page for more information.