The tweet, sent out early on Tuesday afternoon, saw the former actor and now MP for Spain's centrist social liberal party UPyD making fun of Rajoy's habit of slightly slurring his final 's's.
In the Twitter message, Cantó referred to the Spanish leaders recent announcement that he would appear in the country's parliament to answer questions about an illegal slush fund allegedly run by the ex-treasurer of Spain's ruling Popular Party (PP).
Rajoy said on Tuesday he would make that appearance on August 1st.
"You don't want an appearance?" wrote ex-model Cantó in a tweet in which he pretended to be the Spanish leader.
"Well I'm going I'm going to do it on August 1st and see how you organize that with your families," said Cantó, referring to the fact that most people are on holiday at this time of year.
Rajoy suffered a traffic accident in 1979 which disfigured his face.
The Spanish leader now wears a beard to cover the scars, according to Spain's El Mundo newspaper.
But the surgeon who conducted the operation has said that Rajoy's reconstructive lip surgery has nothing to do with the way he speaks.
Cantó, nonetheless, felt compelled to say sorry an hour after his initial tweet.
"I apologize for my imitation before, the truth is it wasn't fitting," he said.
Cantó also kicked up a storm in April when he compared Spain's language laws to paedophilia.
During an interview with Jotdown magazine, Cantó, originally from Valencia, was asked if he thought he was right to call the Popular Party’s stance on introducing Spanish into the Catalan educational system “linguistic fascism”.
The former TV star responded by saying: “There are limits, they can’t curtail my freedom. In the same way as you can’t let paedophiles get away with what they do.”