Do you say
Der Text, den ich gelesen habe, handelt sich um einen türkischen Jungen, der Metin heißt.
Handelt sich um here means is about, doesn’t it?
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So your example should be corrected to:
Der Text, den ich gelesen habe, handelt von einem türkischen Jungen...
“Sich handeln um” is a somewhat complicated construction with a completely different meaning. For example,
Bei dem Text, den ich gelesen habe, handelt es sich um eine Kurzgeschichte.
would be a slightly convoluted way of saying
Der Text, den ich gelesen habe, ist eine Kurzgeschichte.
As long as you do not want to say that the text is a boy, that construction is out of place here.
I have to say however, that I find some of the constructions in the Duden unusual (e.g. 5a and 6b). For example, according to 5a, you could also say
Der Text, den ich gelesen habe, handelt um einen türkischen Jungen...
This is marked as “gehoben” (of a higher register) in Duden. I do not think that I have encountered this before, and I would advise you not to use it.