Rogándote comes from the Spanish verb 'rogar', meaning 'to beg' or 'to plead'. It is a strong, emotional word that conveys real desperation, not just a simple request.
In this song, the lyrics say "Yo sé cómo terminaré, yo rogándote" ("I know how I'll end up, begging you"), using rogándote to admit, almost with resignation, that he already knows he will end up pleading for this person's love.
This is a drunk-dial song, and Nicky Jam is honest enough to say so in the first breath: "Perdona si te estoy llamando" (Sorry for calling you), then "Es que el efecto del alcohol por fin me está pegando" (it's just that the alcohol is finally hitting me). He already knows how the call ends before he makes it. "Yo sé cómo terminaré, yo rogándote" (I know how I'll end up, begging you). The advice in his own head is the title: "Algo me dice 'olvídala'" (Something tells me "forget her"), because she has moved on and, as he puts it, "aunque duela, nunca volverá" (even if it hurts, she'll never come back).
What makes it sting is that he never pretends he will take the advice. "Porque la volveré a llamar" (Because I'll call her again) is a promise, not a fear, and he apologises in advance for the next time. The jealousy underneath comes out in small, specific pictures rather than big statements: "Cuando aventuré por toda tu piel" (When I ventured all over your skin), and then the thought he cannot sit with, "Y ahora andas con otro tocándote" (And now you're with another guy, and he's touching you). Reggaeton usually plays this kind of thing as swagger. Here it is a man at three in the morning with a phone in his hand, losing.