Lawmakers have asked for a pardon three times in the past decade, most recently in March, though none has been successful. The Justice Department has said its general policy is not to process posthumous pardon requests, and the White House declined to comment on the most recent congressional resolution.
So on Monday, to mark what would have been Johnson's 135th birthday, his relatives and supporters gathered in Galveston to honour him and record a video to go straight to Obama.
Leon Phillips, president of the Galveston County Coalition for Justice, which helped to spearhead the effort, said yesterday that the video adds another layer of support.
"Not only is it coming from Congress, but it will be coming from the citizens of the United States if we can just get everyone to click on that like button," he said. "President Obama's father could have been convicted of the same thing because he was married to a white woman and they travelled all over the world and from state to state."
Johnson's great-great niece, Linda Haywood, said Johnson was "railroaded" by authorities.
"I didn't know the man was my uncle until I was 12 years old, that's how ashamed my family was of the fact that he went to prison. A pardon would erase the shame and the stigma and allow us to hold our heads up high because we know what a great man he was," Haywood said in the video.
"I'm asking President Obama as the first black, African-American President to give my uncle a pardon," she said. "A lot of times when he would come to his sister's house or his mother's house he had to sneak at night with his white girlfriend or his wife because of the times that they lived in."
Authorities first targeted Johnson's relationship with Lucille Cameron, who later became his wife, but she refused to co-operate.
They then turned to his former mistress, a prostitute named Belle Schreiber, to testify that Johnson had paid her train fare from Pittsburgh to Chicago, for immoral purposes.
Johnson skipped bail and fled the country after his conviction, but in 1920 he agreed to return and serve his sentence.
So far, the YouTube video hasn't had too many hits. But Haywood and other relatives are determined to get a pardon to clear Johnson's name.
"The colour of your skin should not determine who you - or how you - love," Haywood said in the video.
Jack Johnson
* Born in Galveston, Texas in 1878 and died in a car accident in Franklinton, North Carolina in 1946.
* Johnson became the first African-American to win the world heavyweight crown in 1908, knocking out reigning champion Tommy Burns. He had 123 bouts, winning 77, 48 by knockout, drawing 14, losing 13 and 19 no decisions.
* He held the title until 1915, and boxed until he was 50.
* Johnson was inducted into the International Boxing Hall of Fame in 1990.
- AP