Is there an app that lets me use an iPhone as a mouse?

To the best of my knowledge, the answer is no. Of course, without trying out every single mouse app in the App Store, I can't be 100% certain.

I can tell you that I've been a long time user of Mobile Mouse. They have about the best mouse/remote control app I've found. They put a lot of effort into trying to get the app to work like a real mouse, and eventually decided that it couldn't be done, at least not with an acceptable level of performance (see FAQ #6). They decided on the "air mouse" mode instead, and though it doesn't work like a real mouse, it does work very well for what it is.

Best of luck in your search, and of course if you do find such an app, please let us know!

Remote Mouse is a free app downloadable from the iOS App Store, which can act as a trackpad, "Wiimote" style controller, or keyboard.

You also have to download the Remote Mouse Server app from the Mac App Store onto the Mac you wish to control.

This app DOES NOT work as a mouse in the traditional sense. The closest feature to a mouse that is offered is that of a "Wiimote" style controller, where the user can wave their iPhone in the air while pointing it at the screen to move the cursor.