The tweet posted by Robin Traquair, who is standing for the Dalkeith ward in the Midlothian local election, showed a picture of the Queen taking part in her Olympic opening ceremony stunt with the 007 actor Daniel Craig.
Craig/Bond is quoted as saying: “So Ma’am, Nicola Sturgeon?”
Her Majesty replies: “Just make it look like an accident 007.”
A SNP spokesman said: “This tweet is utterly distasteful and comments like these are deeply disturbing, particularly in light of the killing of Jo Cox last year. They have no place in our political discourse and the constituents in Dalkeith will be sure to agree.”
The Conservatives pointed out that the tweet was posted in 2015 – before the killing of Ms Cox in 2016.
A Conservative spokesman said: “We will be speaking to the individual concerned about this unacceptable Tweet. However, it does seem questionable for the SNP to link this to the Jo Cox murder, when the tweet was made one year earlier.”