Platner won as expected in Tuesday's primary election - despite information emerging in the spring that he had been unfaithful to his wife and had sent text messages with sexual content to a number of women.
The former Marine's tattoo, which could be seen as a Nazi symbol, has also been questioned.
Every day I wake up and try to be a little better and a little kinder, Platner said in his victory speech - in which he also promised political change.
In the fall midterm elections, Platner faces Susan Collins, who is hoping to be re-elected to the Senate for a sixth time. The politically centrist Collins is the only Republican senator from New England.
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