The Chicago Manual of Style acknowledges that both italics and quotation marks are valid, but recommends italics (emphasis mine):
Q. How do you set apart a word as a word in a sentence? As in “We are all aware the word fat could be offensive.” Would fat be in quotes, italicized, or just left alone?
A. Words used as words must be set off somehow—otherwise the meaning
of the sentence can become ambiguous or even unintentionally funny:
He wrote the essay using fat instead of lard.
It was ironic that the misspelled word was right.
He wrote the essay using fat instead of lard.
It was ironic that the misspelled word was “right.”
Chicago favors italics, but quotation marks are also fine.
According to Purdue OWL, one should use italics:
Italicize a word when referring to that word.
- The word justice is often misunderstood and therefore misused.
This is in contradiction to the recommendation to use quotes (or double-quotes) in the accepted answer to a related Stack Exchange question, but I would consider those references less authoritative: How do I refer to a word? Of particular note, the accepted answer referenced Grammar Girl, but this Grammar Girl page specifically explains that it's a style choice:
Double quotation marks can also be used when you are writing a sentence and you want to refer to a word rather than use its meaning. Since I talk about words a lot, this comes up in almost every Grammar Girl episode. It's a style choice. You can use italics or double quotation marks to highlight words, but we use quotation marks on the Grammar Girl site because it takes a bit of extra time to italicize words in our content management system.)
Short answer: You see both, and both are accepted/acceptable. But I would use italics as a general rule, all else being equal.
Grammar Tips articulates this take on it nicely:
...you will want to set it off either with quotation marks or with italics.
If there are many such references, italics are preferred because they create a much less cluttered look. And if the reader is likely to want to make note of "vocabulary" terms (as in a book or article on a technical subject), italics serve to highlight the important terms more effectively.
But for the occasional reference to a word as a word or to a word being used in some specialized way, quotation marks serve nicely.