It is the right of anybody to file an ethics complaint against any senator. In fact, that was the advice to him by Sen. Gordon when he visited him in his detention place.
The Constitution, however, is clear on the matter. Thus, Article VI states:
SECTION 11. A Senator or Member of the House of Representatives shall, in all offenses punishable by not more than six years imprisonment, be privileged from arrest while the Congress is in session. NO MEMBER SHALL BE QUESTIONED NOR BE HELD LIABLE IN ANY OTHER PLACE FOR ANY SPEECH OR DEBATE IN THE CONGRESS OR IN ANY COMMITTEE THEREOF.
Therefore, it is his right to waste bond paper and ink. Anyway, he has the money to pay his lawyers even if it’s tantamount to an exercise in futility and stupidity.