You can use " Earworm " which means: a song or melody that keeps repeating in one's mind
ell.stackexchange.com/users/48965/helen
You could say the song is "stuck in your head".
I haven't found a dictionary listing the phrase, but here's a Time article on the subject, with the title "Why Do Songs Get Stuck In Your Head?"
For example usage, to express "after listening to a popular song you can't stop repeating it in your head" I would say: I heard [popular song] on the radio, and now it's stuck in my head.
"Earworm" is a very related term.
Essentially, if a song gets stuck in peoples' heads frequently then it can be called an earworm.
On the other hand, the phrase "stuck in your head" is how you talk about a specific time when it happened, such as "it's stuck in my head right now" or "it was stuck in my head when I left yesterday".
ell.stackexchange.com/users/59254/Kamil Drakari
The German Wikipedia on "Ohrwurm" lists earworm as a loanword from German.
To be more precise, it is a calque (thanks @PLL), a word for word translation of the two parts Ohr and Wurm (ear and worm).
It also has other suggestions:
sticky music, head music and the English Wikipedia on loanwords calls it catchy tune.
Based on the comments by two native speakers and their up votes - those suggestions are even less used.
Catchy tune is better used for an appealing and memorable tune rather than a song which is stuck in your head at the moment.
ell.stackexchange.com/users/70410/Arsenal
Another term I've hear used is " song virus ".
Surprisingly to me, I couldn't find this listed anywhere other than Urban Dictionary , but it's definitely a usage I've heard as an American native speaker.
ell.stackexchange.com/users/31687/fyrepenguin
You can use hook : Catchy part of a song that draws in the listener, not necessarily the chorus.
ell.stackexchange.com/users/81080/Wladislove Schegoleff
The word I've heard is " earbug ".
Here's the example there: Person 1
: Why are you acting so weird?
Person 2:
Sorry, I have an earbug.
I can't get this stupid Metallica song out of my head.
ell.stackexchange.com/users/71131/KYHSGeekCode
Sometimes after listening to a popular song you can't stop repeating it in your head. Is there any term for this in English? You can't say the same in Russian using one word.
Does the English language have a word explaining a song in your head that you can't stop singing?
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<word-request><phrase-request><expressions><synonyms>
ell.stackexchange.com/questions/177120
ell.stackexchange.com/users/81028/Maryia Beliankova  
A song that is "stuck in your head" can be described as an"earworm" or "earbug". A song can also  be described as having a "hook" or beign "catchy". Earworm, earbug, song virus, stuck in my head.
Earworm' or 'earbug' can be used, or you could say that the song is "stuck in your head". Song virus' is listed in Urban Dictionary, but is less common. The hook of a song could refer to the catchy part that draws in the listener.