The text on which I found the following sentence is here: http://watanoc.com/post-1608-gozira So... There's a part where it says: 『すごく面白い』とネットで評判です So my question is what does the と particle do in this sentence? And also why "すごく面白い" is between these symbols "『 』"
So, as Micah has said, this
と is indeed the quoting particle.
That said, Japanese is a lot more flexible with the grammatical concept of quotation and how it fits into sentences than English is. Quotes can attach to things that you wouldn't expect them to in English - like in this case, the noun
If you look here (and ignore all the examples involving
名声と評判 because that's the exhaustive listing
と), you can see that
~と評判 is a construction roughly meaning "have a reputation for". Jisho's second example sentence is in much the same vein.
In short, this comes out to something like:
It has a reputation online for being super interesting/funny
Or more in more colloquial English:
Everyone online says it's super interesting/funny
The quotation marks (『 』) are simply there to disambiguate the fact that quotation is going on; the phrase would be comprehensible (but perhaps not as immediately obvious to learners of the language) without them.
According to https://jisho.org/word/と:
と can be a particle used for quoting (with speech, thoughts, etc.)
Concerning 『 』, according to https://www.japanesewithanime.com/2017/05/quotation-marks-japanese.html:
There is no difference between how 「」 and 『』 affect a phrase. They are both just quotation marks and don't impact the grammar, add nuance, or whatever. There is as much difference between them as there is difference between ' and ".
EDITED I could not find the phrase on the page you linked, but @DariusJahandarie pointed out it's actually on the page without kanji, with regular quotes 「」, and with extra whitespace.
「すごく おもしろい」と ネットで ひょうばんです。
I've also removed my incorrect translation, please see the answer by @Mindful