The phrase "to become a senator" means to be elected or appointed to a position as a member of the Senate, which is one of the two chambers in the United States Congress. Full definition
From the time Huntley became a senator in 2007 «she was looked at with suspicion, since she was so clearly a «transactional» person looking to cash in,» said a source who has been close to Schneiderman and Huntley. (nypost.com)
This legislation took effect during the 2002 General election and Ed Mayne became the Senator for the current 5th Senate District. (en.wikipedia.org)
Gillibrand has reversed positions on some gun legislation that she herself sponsored before becoming a senator. (nbcnewyork.com)