deepL translates "J’en ai la larme à l’œil" to "I have a tear in my eye" (or in more natural English, "It brings tears to my eyes").
I don't know what the "en" is there for. "J'ai mal à la tête" is a similar sentence, but it doesn't use an "en".
What is the "en" replacing in "J'en ai la larme à l'oeil"?
I saw "J'en ai la larme à l'oeil." in a reddit comment. I can't remember the rest of the context, but it was a very short reddit comment where "It brings a tear to my eye" made perfect sense.
EDIT
A user voted my question to be closed, because they claim that this is a duplicate. I am now obliged to prove that linked question is not a duplicate of my question, in order to prevent my question from being closed.
The linked question asks: "Meaning of “en” in “qu'elle ne voulut plus en porter d'autre”?".
My question asks "What is "en" replacing in "J’en ai la larme à l’œil?".
The answer to the linked question says, in effect, "Given the context of the sentence you're asking about, the 'en' is required; the sentence would not make sense without the 'en' ".
My question is about an entirely different sentence, in an entirely different context. I, in fact, don't understand the answer in the linked question, and even if I did, it is not obvious how to apply it to my sentence.
Jst because two questions ask about the use of "en" in a sentence, doesn't mean that they are duplicates of each other and that one deserves to be closed.