"Television newscasters use the phrase, ‘Take a listen,’” said Diane Morlock of Enid as Buck checked her windshield wiper reservoir at Curly’s Soonerco. "Is this correct?”
It depends on how lofty you want to be and how much scorn you want to endure from people who frown on any descent into informality.
Normally, "listen” is a verb, but Merriam-Webster’s says it has been used since 1738 as a noun meaning "an act of listening.” The American Heritage Dictionary agrees, and it illustrates with this example: "Would you like to give the CD a listen before buying it?” Encarta sanctions the same usage but labels it "informal.”
The Internet abounds with examples of "give a listen” and "take a listen.” Most are in informal contexts, and many are from blogs, where language is usually informal and rules of grammar loose.
"Take a listen” may be considered a form of media-speak, which is not the most exalted level of language. It says nothing that a simple "listen to this” doesn’t say, but it says it in a slangy sort of way that some may consider less stuffy.