Cynthia Nixon has landed her first endorsement by a Democratic elected official.

Brooklyn City Council member Carlos Menchaca announced his support for Nixon’s insurgent bid against Gov. Cuomo during a joint video appearance posted Monday in which the “Sex and the City” actress vows to push for driver’s licenses for undocumented immigrants.

“I proudly endorse Cynthia Nixon to be our next governor of New York. Cynthia stands with immigrants, people of color, and the working class across our state and will fight for respect and dignity for us all,” said Menchaca, the city’s first Mexican-American elected official.

Menchaca, who also is gay, is the first prominent city elected official to endorse Nixon.

While a breakthrough for Nixon, most of the New York’s Hispanic electeds are lining up with the governor.

Cuomo took his third trip to Puerto Rico this week to monitor hurricane recovery efforts, where he was accompanied by Bronx Borough President Ruben Diaz Jr. and Assemblyman Marcos Crespo, also the Bronx Democratic Party chairman.

Rep. Nydia Velazquez, who represents some of the same neighborhoods as Menchaca, recently told The Post she was “100 percent in support” of Cuomo’s re-election.

The campaign to provide driver’s licenses to undocumented immigrants has been controversial for a decade.

Former Gov. Eliot Spitzer first pushed the issue, but retreated under a firestorm of attacks across the state, including from Democrats.

It is not an issue Cuomo has championed.

The campaign is popular in some immigrant communities and lefty political circles. But it’s chances of passing the Legislature, particularly in a Republican-led state Senate, is slim.

Nixon said it’s a vital pro-immigrant measure.

“New York needs to lead the way to protect immigrants. We’re lagging behind. Isn’t it time we change that?” she says in the video.