Firas Shehadeh, founder of the group Turabyeh ("Of the Soil"), filed an injunction with the Haifa District Court on Monday stating that the song had been used without permission, Iyad Jubran, the group's attorney, told Reuters.
"They were stunned by Likud's shamelessness and outright theft," the Israel-based Jubran said.
Representatives for the Likud party and Netanyahu declined to comment.
The song, entitled 'Gorbeh' (Alienation), is being used in a 40-second online video posted on Netanyahu's YouTube channel.
The Israeli driver replies: "Turn left."
The message appears to be that if the center-left defeats Netanyahu's right-wing party in the March 17 parliamentary election, ISIS will take over.
Shehadeh said he learned of the clip from friends on Saturday, shortly after it was posted online.
"I was shocked, it was craziness," he told Reuters by phone from Spain. "We are against ISIS and against Israel."
The court petition says the clip creates the impression that the group supports ISIS and could expose them to reprisals by those who oppose Islamic State. Its use in the campaign of an Israeli right-wing party could also deter their fans.
Turabyeh has four members, three of them descendants of Palestinian refugees, millions of whom now live in Jordan. The song is about their political alienation and longing for a return to their Palestinian homeland, Shehadeh said.