False, they are only allowed 2 consecutive terms.
“No person who has been elected for a full term to the
Senate two consecutive times shall be eligible for election or
appointment to the Senate for a third consecutive term.”
In other words, if approved by two-thirds of the members of both the House and Senate, and if ratified by three-fourths of the States, then the congress shall limit the United States Senators to two full, consecutive terms (12 years) and Members of the House of Representatives to six full, consecutive terms (12 years).