The only two rickers who I can think of who have repositioned themselves into singing old standards are Rod Stewart and Linda Ronstadt. Are there any others?
Elvis?
Yeah. I think he counts.
Iggy Pop has been known to croon. Seriously. For instance, he (like both Rod Stewart and Linda Ronstadt) has recorded a cover of “I’ll Be Seeing You”.
With the release of* Kisses on the Bottom*, I think Macca belongs on the list.
Who is Macca? The first page of Google hits turns up nothing.
Paul McCartney. British tabloid slang.
Jeez, I better order a wheelchair and oxygen bottle soon, while my brain is still capable of it.
Sting, Steve Tyler, Toni Tenille, Paul McCartney, Elton John, Queen Latifah, Chaka Khan have all recorded standards. Willie Nelson was one of the people who started the trend with 'Stardust" in 1978.
Macca was John’s nickname for Paul, picked up by the press and used by many of his friends. (it is also used in the UK as a nickname for people with last names that start with *Mac *or Mc)
Actually, Ringo was way ahead of the curve–he released Sentimental Journey back in 1970
But none of them, with the possible exception of Steve Tyler, are rockers.
Elvis Costello has tended toward the croon of late (although he has always had some croony numbers in his repertoire).
Bryan Ferry of Roxy Music fame, their debut album was a wild and experimental but solidly rocker outing that showed a wide range for Ferry’s vocals. With the departure of Eno Ferry’s romantic crooning took center stage until their final album Avalon which has not one drop of rock in it.
Robert Plant did some solo crooning after Led Zeppelin.
David Lee Roth?
an NSFW might have been appropriate, seeing as how there’s some toplessness in the video. Not that I object to toplessness, or anything… 
Brian Setzer has thrown a few tunes that might qualify on his retro-swing Brian Setzer Orchestra recordings, like “A Nightingale Sang in Berkeley Square.”
Little-known fact: Paul McCartney once had a rock band. It’s true. Pretty sure that Sting fellow did too.
I guess you could call it that.