See this news report from Arizona. A snippet: “Although McCain is a federal officeholder not bound by the Arizona Constitution’s recall provisions, he has signed a voluntary pledge on file with the Secretary of State’s Office agreeing to resign immediately if defeated in a recall election.” Joshua Spivak writes regarding this article:

Here is also a couple of paragraph from my article on the California Recall dealing explaining the recall of federal officials.
Congresmen Mark Neumann signed a petition to recall Wisconsin’s two Democratic Senators over their position on abortion. Julie Cohen, “Mark Neumann, Republican Hothead,” The Economist (May 3, 1997). The courts ruled that a U.S. Senator cannot be recalled. In addition, in 1995, California Senatorial candidate Michael Huffington, who spent $30 million of dollars of his own money in a losing Senate bid in 1994, and whose ex-wife Arianna ran for election in the Davis Recall, was set to hold a press conference calling for the recall of Senator Dianne Feinstein, the winning candidate in the election. According to the San Francisco Chronicle, Huffington did not hold the press conference after he “was advised that, by law, a U.S. Senator cannot be recalled” Susan Yoachum “Huffington Plan for a Recall is Recalled,” San Francisco Chronicle (February 27, 1995).
There has also been some discussion of bringing the recall to the national level. A 1987 poll run by the Twentieth Century Fund found popular support for the extension of the recall to federal officials. In 1996, Representative Peter Hoekstra introduced a package of “Voter’s Bill of Rights,” which would include recalls for Senators and Congressmen, and there have been occasional calls to recall U.S. Senators ( H.J. Res. 86, 105th Congress).
As a side note, the articles of confederation government did provide for a recall, and there was a lot of pressure to give states the power to recall Senator (prior to the 17th Amendment).