Jared Leto first got known as a teen actor then became very successful as a singer then he won the Oscar.
It may be a joke today, but it has a long history. Browse around a used record store, or YouTube, and you will find a lot of albums by celebrities you never imagined could sing.
Robert Mitchum did an album. (If you can stomach the thought of a rich white yank singing calypso, it’s really not bad.)
Before he became leader of the Nation of Islam, Louis Farrakhan had some success as a musician, under the stage name “The Charmer”.
Strangely enough, both of them covered Roaring Lion’s “Ugly Woman” (which most yanks have never heard of, though many of us are familiar with Jimmy Soul’s version, “If You Want To Be Happy”.)
What, you didn’t like “The Ballad of Bilbo Baggins”? 
Phil Collins, in “Buster”,
Barbara Streisand did a lot of both. So did Doris Day. Dean Martin. Frank Sinatra.
Gordon Sumner was gross in a sorta Sting-like way in Brimstone and Treacle.
Ironically, Phil Collins started out as a child actor, albeit not a very successful one. (His most notable role was as an extra in A Hard Day’s Night.) I remember the time he guest-starred in an episode of Miami Vice; good lord, he was terrible.
I don’t think either Sinatra or Martin were ever taken seriously as actors. Good point with Streisand, though.
Also, there’s Mark Wahlberg, who seems to have successfully made the transition from one-hit wonder pop star to A-list Hollywood actor. Although, as mentioned upthread, hip-hop isn’t really music. 
Sinatra won the Oscar (supporting actor) for “From Here to Eternity” and the Golden Globe for “Pal Joey”. Martin starred in several (terrible) movies (with Jerry Lewis), all boxoffice hits, before becoming known as a singer.
Jerry Lewis was great in King of Comedy. His new one, Max Rose, I’d be curious to check out.
Kris Kristoffersen was great as one of the all-time great baddies, Charlie Wade in “Lone Star”
It occurs to me that, although people are somewhat dubious of singers who want to become actors, and even more dubious of actors who want to become singers, they really quite enjoy genuine acting/singing double threats. That’s why I am always supportive of any young actor who decides to crank out an album. It may be – and almost certainly is going to be – awful, but it’s a great way to get the public used to the idea that you do both. No one will try to cram you into the acting box or the singing box if you are always hopping back and forth.