Trump asked Kushner to serve as a senior adviser to the president.
Unlike cabinet positions, the job of adviser does not require approval of the United States Senate.
Six members of Congress are questioning Kushner's appointment. All six belong to the Democratic Party.
The lawmakers wrote a letter to Attorney General Loretta Lynch and the U.S. Office of Government Ethics. They noted that a 1967 law bars a public official from appointing a family member to the same agency in which the official serves. They also asked the Justice Department and ethics officials to investigate possible conflicts of interest.
Jared Kushner is married to Donald Trump's daughter Ivanka.
Lawyer Jamie Gorelick is advising Kushner on legal issues. She said the law does not affect the president because the White House does not fall under the definition of an agency.
The lawyer also said that Kushner plans to sell all his foreign investments and his financial interests in an investment company and an office building in New York. He also will resign as head of Kushner Companies and as the publisher of The New York Observer newspaper before working for the Trump administration.
The six lawmakers questioned Gorelick's statement that Kushner would remove himself from decisions involving his remaining financial interests after leaving his companies. They said he would still have investments that could be affected by government policy that he influences.
Aides to Donald Trump said that, as a presidential adviser, Kushner will work mainly on issues involving trade and the Middle East. They said he will work closely with Chief of Staff Reince Priebus and Chief Strategist Stephen Bannon.
川普的助理们表示，作为总统顾问，库什纳将主要负责涉及贸易和中东方面的问题。他们表示，库什纳将同白宫办公厅主任赖因斯·普里巴斯（Reince Priebus）以及首席策略师斯蒂夫·班农（Stephen Bannon）密切合作。
Legal experts are offering differing opinions about whether the appointment of Trump's son-in-law violates the 50-year-old law.
Kathleen Clark is a law professor at Washington University in Saint Louis, Missouri. She said her understanding of the law is that it does affect the president.
"Congress didn't in this law carve out an exception for the White House," Clark told the Associated Press. She said it governs the presidency, the legislature, the courts and the District of Columbia government.
But Indiana University professor Gerald Magliocca said he did not think the law could be used to restrict the president's team without risking constitutional problems.
"It's hard to see why Congress has the authority to limit presidential staff members," he said.
I'm Caty Weaver.