The phrase "a degree of popularity" is correct and usable in written English.
You can use it when referring to a degree of popularity or recognition that something has. For example, "This band has achieved a degree of popularity in recent years due to their hit single."
According to the Pew poll, these three leaders all share a degree of popularity in Italy.
She also earned a degree of popularity as a pinup model during World War II.
On Thursday evening, they present "L'Ascension" and on Friday the huge "Turangalila Symphony," one Messiaen work that can indeed be said to have achieved a degree of popularity.
Late in his career, Dr. Sanders achieved a degree of popularity as a co-host of a PBS series on ancient cultures.
On the other, Peres is Israel's elder statesman, who, very late in his life, has attained a degree of popularity that eluded him throughout his earlier career.
Although his folk-song settings have won a degree of popularity, Canteloube's original works, which include the operas Le Mas and Vercingétorix (performed at the Paris Opéra in 1929 and 1933, respectively), have been neglected.
But if this was a good day for Osborne, it is only in the context of politicians struggling to have credibility or any degree of popularity on social media spaces.
Timorese coffee has gained a degree of international popularity, with Starbucks, among others, a buyer.
According to the most recent Times of Israel poll, he retains a degree of personal popularity (although he has been losing voters from his rightwing core and picking up support from the left and centre).
In the first real crisis of his papacy, Francis finds himself in the position of enjoying a rare degree of popularity among the public but facing an unusual degree of dissent within an institution generally so respectful of hierarchy.
In the 18th and 19th centuries, shadow plays called ombres chinoises ("Chinese shadows") achieved a limited degree of popularity, especially in France.
