Cop Singing 'Shake It Off' -- Dash Cam Footage is Fake ... But It's Still Awesome!

The viral video of a cop singing "Shake It Off " while on patrol is NOT legit dash cam footage ... TMZ has learned -- but if that stops you from watching, then you clearly have no soul.

The video has been blowing up the internet Saturday ... and already racked up over 400K views on YouTube in less than 24 hours -- but the Dover PD tells us the whole thing was produced ... despite the chyron saying otherwise.

We're told the officers wanted to film their Taylor Swift tribute to celebrate the success of the station's Facebook page ... and show a lighter side of law enforcement.