I heard someone says
"You have me worried".
Is it same as "You made me worried"?
Any difference in nuance?
They are similar. They are both causative sentences. However, the first sentence uses the present tense. It will be interpreted as a stative meaning. It describes a situation. It means that I am worried now because of something you've said or done. The second sentence means that something you did in the past made me worried in the past. It has more of a dynamic feeling as opposed to a stative feeling. The second sentence does not say whether I'm still worried. I'm probably not, but I could be.
There's no real difference (aside from tense: "you have me worried" is present tense (I am worried about you, right now), and "you made me worried" is past tense (I was worried about you in the past)).
However, "have me worried" is unlikely to be what you heard -- the usual phrase is "you had me worried." For most speakers I know, the present-tense way to express that situation would be "I'm worried about you." (It's not impossible someone would have a quirky turn of phrase, but it would be uncommon.)