I'm not a native speaker but ... I think that since 上癮 means "become addicted to", it's saying love has made people become addicted. chinese often uses this verb+object pair, like 吃飯 means literally eat+meal/rice, but this pair itself is almost a pseudo-verb itself meaning eat. so sometimes you can see them split with other particles. 你吃了飯嗎？ － (did you eat?) but you can also put it after the verb+object "pseudoverb": 你吃飯了嗎? I'm fairly confident this is right, waiting to see if a native speaker corrects me.

爱就让人上了瘾 = Love can become addictive 上瘾 = rise to addiction (verb + noun coupling) 了 indicates completion. It's a complicated particle, so I suggest a good dictionary with lots of explanation in it for that one.

The song name is "美人计". Thanks a lot everyone :). I don't know how to choose a best answer, because you were all quite helpful! I think I have a better idea of what it means now, so that will help me when listening to the song.

FYI, in english I think the term "get hooked" is appropriate - a little less 'formal' sounding than 'addiction'.

Can you tell me the song name? We often say" 爱，让人上瘾". It means"when you love someone,we are more and more fascinating to her and can't get out of it.