The singer put his own spin on the track, which features on West's forthcoming new album, reported Billboard.
Jonas tweeted the rapper with a link to the cover, writing: "I love this song so much I had to sing it myself..."
The 22-year-old will release his eponymous solo album on March 9.
Meanwhile, West has said that the follow-up to Yeezus is "80 per cent done" and will have a surprise release.
Jonas will host the 2015 Nickelodeon Kids' Choice Awards on Saturday, March 28.
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