Does stock Android have a panorama camera feature? I was wondering if Android has any panorama-like feature like how iOS does?
This depends entirely on the OEM and what features they decide to put in their devices.

However, I've used a panorama feature since the beginning (2.3 Gingerbread) on my Nexus S, and have had it all the way till my 4.2 Galaxy Nexus, so I can say that the stock Android camera app has panorama, at least 2.3 onwards.

Beyond that, device specific panorama is dependent on the OEM.

You could always use third party apps, like this one, which supports Android 2.1 and above.