The profile picture on the official Twitter account for the force in Edinburgh was also changed to include a “Yawn” sign.
The post, tweeted by verified account @EdinburghPolice, read: “I just added @scotlandinunion’s #Yawn badge as I am tired of the @theSNP still going on about #Indyref2.”
It is understood the incident on Saturday was put down to human error and the image and post have been removed.
Chief Inspector David Robertson said: “We’re aware of this tweet and it was deleted immediately. All officers will be reminded of the need to use social media responsibly.”
The Yawn campaign was launched by pro-UK group Scotland in Union.
Users can follow a few instructions to have the icon added to their page and the message automatically tweeted out to their followers.