The petition, which has a goal of 150,000 signatures, endeavours to get the attention of US president Donald Trump, the US Senate, as well as other government bodies and senior politicians.
Kyle Siler, who started the petition, gave several reasons why Billy Graham deserved a national holiday.
He said: "Mr Graham's counsel was sought by presidents, and his appeal in both the secular and religious arenas is evidenced by the wide range of groups that have honoured him, including numerous honorary doctorates from many institutions in the U.S. and abroad.
"Help us with our cause of setting a national holiday to remember this great man."
Rev Graham died at the age of 99 on 21st February in his sleep. His funeral on the 2nd March was attended by two thousand people including Mr Trump.
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