There is no limit on the number of terms a Senator in the United States Congress can serve. However, there have been attempts to pass a Constitutional amendment that would impose such a limit.
The Articles of Confederation, a document outlining the political structure and laws of the early United States, mandates term limits for individuals serving in federal legislative bodies. The Constitution, which replaced the Articles as the law of the land, does not address any such limits. Under the Constitution, in order to run for Senate, one must be at least 30 years old, a citizen of the United States and reside in the state where the candidate is running for office.