He told a press conference “every Floridian should be concerned there may be rampant fraud”.
Provocatively Mr Scott added: “I will not sit idly by while unethical liberals try to steal this election.
“I am proud to be the next Senator for the great state of Florida.”
He accused his opponents of “mysteriously finding more votes”.
He is specifically taking action against Supervisor Brenda Snipes over Broward County’s failure to complete its count of midterms votes.
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Broward County is the only one of Florida’s 67 counties which is yet to complete its initial count.
Mr Scott is currently leading by a mere 17,000 votes.
His claim to have won the election was backed by President Trump who tweeted: “Law enforcement is looking into another big corruption scandal having to do with electoral fraud in Broward and Palm Beach.
“Florida voted for Rick Scott!”
Mr Scott’s rival, sitting Democratic Senator Bill Nelson, responded: “Rick Scott’s action appears to be politically motivated and borne out of desperation.”
Democrats believe there is an issue with how votes were calculated in Broward county and Palm Beach, both strongholds for the party.
They hope votes from these areas, once they are recounted, will allow Mr Nelson to leapfrog his Republican rival.
Election officials in Broward County, the second largest county in Florida, are refusing to confirm how many votes were cast or how many they have less to count.
A hand recount will take place as the difference between Mr Nelson and Mr Scott is within a 0.25 percent margin.
The legal challenge is Mr Scott’s first public comment since claiming victory on election night.
However, his self-proclaimed victory has not been confirmed by either local or national media.
Mr Scott’s team released a statement yesterday saying: “It is sad and embarrassing that Bill Nelson would resort to these low tactics after the voters have clearly spoken.
“Maybe next, he’ll start ranting that Russians stole the election from him.”
A recount is also expected to take place in the Florida governor race between Republican Ron DeSantis and Democrat Andrew Gillum.
Mr DeSantis is currently leading by 36,000 votes.