The Nexus 7 may not come with a stock Camera app, but a clever hack over on XDA brings it back and even allows it to record 720p footage. Provided you’re rooted, of course.
You’ll need two downloads to enable video recording: A camera mod file that you can flash via your custom recovery, which will patch the OS to enable support for video recording, and the Camera Launcher app from the Play Store. This will bring back the Camera shortcut. The app itself is actually on your device already (since other apps use it), but the icon was simply removed because the slate has no rear sensor.
We haven’t been able to test this personally, but several users over on XDA have reported success with this method. Give it a shot and let us know how well it works for you!