Can a Senator be impeached?
Good question. It would probably have to be by the Senate though so good luck there.
I do wonder if senators can be recalled by the people of their state.
Senators can be impeached. So can representatives, and any public official. Article 2, Section 4 of the Constitution says how to do it.
In the history of the US, however, there has only been one impeached from office.
I think there needs to be bunch more.
Looked it up and it has happened once - a Senator Blount in 1779 but it's kind of murky...
The 1799 impeachment of Tennessee senator William Blount stalled on the grounds that the Senate lacked jurisdiction over Blount. Because, in a separate action unrelated to the impeachment procedure, the Senate had already expelled Blount, the lack of jurisdiction may have been either because Blount was no longer a senator, or because senators are not "civil officers" of the United States who are subject to impeachment. At any rate, no other member of Congress has ever been impeached. Of the remaining cases, two did not come to trial because the individuals had left office. Each of the seven Senate convictions has involved a federal judge: in the most recent such case, Alcee Hastings subsequently gained election as a member of the House of Representatives, which had impeached him.
The recall is certainly the better route but I don't know if it's possible with federal elected officials.