Original text - Italian - il tuo dolcissimo viso, i tuoi occhi, la tua...

"rientro" shouldn't be "rientri"?

CC: ali84

No, it's right. Quando rientro = when I come back.

But it's subjunctive, isn't it?

Uhm no, it's just the first person present of the verb "rientrare".
You can use the word "rientro" to express the act of coming back (home, at work, ecc..).
This phrase is: "when I come, I'll run to you to hug you and squeeze you so hard"

What I understand is that "Quando rientro correrò..." will happen in the future.

"When I come I'll run..." That 'come' in English is present subjunctive (even having the same form of the simple present). See what I mean?

Wouldn't it be more correct to say: "Quando rientrerò..." with the futuro semplice? I am just asking.

Oh, I didn't know that Lilian

@guilon: yes, "rientrerò" is definitively more correct, and that's what should be used, but the use of the simple present has become very common.