The line we all know and love and repeat, “Luke, I am your father,” is a misquote. Darth Vader never says that.
That Famous Line From The Empire Strikes Back is Actually a Misquote
Darth Vader never actually says, “Luke, I am your father.” Vader instead says, “No, I am your father.” In other words, this is just one of those misquoted movie lines.
So why does everyone think he says, “Luke, I am your father?” I’ll submit to you that it is not the Mandela effect. Instead my theory is that it was on some TV show or movie comedy along the way said, “Luke, I am your father,” and that was the version that got stuck in the lexicon.
The full quote from the famous scene in The Empire Strikes Back is featured below (in script form and clip form).
Notice Vader doesn’t say the word “Luke” until the end of this exchange. Previously in the exchange he calls him “young Skywalker” and “Skywalker”… which is a little strange since that is his last name too.“Luke, I Am Your Father”
VADER There is no escape. Don't make me destroy you. You do not yet realize your importance. You have only begun to discover your power. Join me and I will complete your training. With our combined strength, we can end this destructive conflict and bring order to the galaxy. LUKE I'll never join you! VADER If you only knew the power of the dark side. Obi-Wan never told you what happened to your father. LUKE He told me enough! It was you who killed him. VADER No. I am your father. Shocked, Luke looks at Vader in utter disbelief. LUKE No. No. That's not true! That's impossible! VADER Search your feelings. You know it to be true. LUKE No! No! No! VADER Luke. You can destroy the Emperor. He has foreseen this. It is your destiny. Join me, and together we can rule the galaxy as father and son. Come with me. It is the only way.
- Empire Strikes Back Script. IMSDB.com.