No. Under long-standing congressional precedent, members of Congress cannot be impeached, because they are not considered “civil officers” of the United States, the officials the Constitution makes subject to impeachment.
The question was settled by the first impeachment in U.S. history. In 1797 the House of Representatives impeached Senator William Blount. Two years later, the Senate concluded that Blount was not a civil officer subject to impeachment and dismissed the articles because it lacked jurisdiction. The House and the Senate have accepted that result ever since, and the House has never again impeached a member of Congress.
The Constitution’s structure points the same way. Officers of the United States are commissioned by the President, while members of Congress receive no such commission, and the Ineligibility Clause bars anyone holding an office under the United States from serving in either chamber. Members can instead be removed by other means the Constitution provides in Article I, Section 5.
Source: Constitution Annotated, Offices Eligible for Impeachment (Legal Information Institute)
Image: West front of the United States Capitol, Architect of the Capitol, public domain, via Wikimedia Commons.