WASHINGTON—Republican Rep. Dana Rohrabacher is weighing the creation of a consulting firm when he leaves government after being ousted by voters in last month’s midterm elections.

Mr. Rohrabacher, who has represented a California district in Congress for three decades, has told senior staff and other acquaintances in recent weeks that he plans to form a company called R&B Strategies with top aide Paul Behrends, according to people familiar with the matter.

A spokesman for Mr. Rohrabacher, who represents Orange County, said the lawmaker hasn’t decided what he will do, but the spokesman didn’t deny the conversations and said forming a company is one of many options the congressman is considering.

The spokesman, Ken Grubbs, said Mr. Rohrabacher’s only definite plans are to move to Maine after the current session of Congress ends in early January and newly elected lawmakers are sworn in.

Mr. Rohrabacher is one of the many lawmakers expected to go to work in lobbying or consulting when they leave government in January. Dozens of Republicans retired or lost their seats this year, making for a crowded post-government employment market for many lawmakers.

In a turbulent political moment with an unorthodox administration and both parties facing upheaval, some former members of Congress may struggle to find their niche.

Mr. Rohrabacher is an unusual case. Long an iconoclast within his party, he has attracted controversy on Capitol Hill in recent years, particularly over his public pro-Russian stances.

The congressman met in 2017 with Julian Assange, the founder of the website WikiLeaks, which U.S. intelligence officials view as Russia’s conduit to distribute material that was hacked and stolen from the Democratic Party in the 2016 presidential election.

Mr. Rohrabacher later tried unsuccessfully to broker a pardon from President Trump for Mr. Assange, who has long been under investigation for the dissemination of stolen material, The Wall Street Journal has reported.

The California Republican is known for other policy stances that are unusual within the GOP, such as the decriminalization of marijuana. In one instance, he worked to bring the president of the Republic of Congo to Mar-a-Lago to meet Mr. Trump during the presidential transition, the Journal has previously reported.

Mr. Behrends, a former Marine who has bounced between Capitol Hill and work as lobbyist, was fired from the House Foreign Affairs Committee by the panel’s Republican chairman amid questions about his contacts with pro-Russian operatives and lobbyists last year.

At the time, Mr. Behrends was being paid by the committee, though he was working for Mr. Rohrabacher. Mr. Rohrabacher then put Mr. Behrends on his personal staff.

During his time in the private sector, Mr. Behrends was the chief lobbyist for Blackwater, the military contractor whose operations during the Iraq War drew scrutiny and legal controversy.

By law, Mr. Rohrabacher will be banned from lobbying his former colleagues for at least a year. But he will be permitted to consult on government-affairs strategy or offer advice on public policy to paying clients.

Write to Byron Tau at byron.tau@wsj.com