Joe Biden indeed secured more popular votes, but factoring in an increase in voters' population, Obama drew a higher percentage of registered voters.
For the 2020 United States presidential election, about 160 million people voted, amounting to a turn out of 66.9%, the highest since 1900, explained Prof. Michael McDonald from the University of Florida, who runs the United States Elections Project.
"The U.S. population has also grown from 304 million to more than 330 million from 2008 to 2020. This means that Mr. Obama received the votes of a greater percentage of Americans — about 23 percent, to Mr. Biden’s 22 percent. Mr. Obama also drew a higher percentage of the country’s registered voters, 48 percent to Mr. Biden’s 45 percent," The New York Times reported.
So, in 2008, 131,313,820 Americans voted out of a total voting-age population of 225,499,000. and in 2012, 129,085,410 voted out of 235,248,000 as per Federal Election Commission's report. Where as in 2020, 159,633,396 voted out of 257,605,088.
Biden indeed secured the highest number of popular votes. But factoring in the increase in the population in general and increasing in the voting-age population, Obama overall drew a higher percentage of registered voters. Therefore, the claim is partly true.