Some of the world’s largest oil companies and the country’s biggest auto maker are joining a group pushing the U.S. government to tax carbon in an effort to slow climate change.

General Motors Co., Exxon Mobil Corp. and BP PLC are among almost a dozen companies joining the Climate Leadership Council, a new organization that advocates replacing many environmental regulations with a simplified tax on businesses that release carbon into the atmosphere. The plan proposes directly paying out this money to all citizens to defray...