No, it wasn't. This often made claim is based on a passage of Phaedrus where Socrates is quoting an Egyptian legend, and the negative judgement of the invention of writing is done by a pharaoh inside that legend being told inside the dialogue.

Besides, the dialogue is not about writing itself, but about writing down political speeches and the consequences and impact of political speeches being read rather than heard.

Also, the dialogue dates from about three thousand years after writing was invented.

Some direct quotes from the dialogue:

SOCRATES: So, it is obvious to everyone that speech writing is not shameful, not in itself anyway (258d)

SOCRATES: We are left with the question of the appropriateness and inappropriateness of writing, and how it may be executed in a worthy or an inappropriate manner. Do you agree? (274b)

And this, a very relevant insight for an age when some are convinced that text analysis should suffice for intelligent work:

SOCRATES: Then a person who thinks he has left a skill in writing behind him, and anyone who, for his part, inherits this on the assumption that something clear and certain will emerge from writing, would be full of enormous silliness, and indeed ignorant of the prophetic words of Ammon in believing that written words are anything more than a reminder to a person who already knows whatever it is that the written words may refer to.

Ironically, the sharpest criticism Socrates made of writing in the often misread Phaedrus was of misreading texts.

Be fair to Socrates though.

We have significantly degraded in our ability to memorize e.g. epic poems or preserve oral traditions since the advent of writing.

I know that sounds trite in retrospect, given the benefits, and that's half the point. But there are real tradeoffs too! For example, culture has a LOT more generation-to-generation turnover as a result of literacy being common, making it unstable.

Was Socrates even wrong, though? There have certainly been millions of words written that were lacking in wisdom and have convinced people of falsehoods to their detriment! When’s the last time you saw a debate be reasonable? devoid of cheap jokes or hot takes? actually change someone’s mind? or the whole audience’s mind?

In the world where we didn’t outsource Western manufacturing to China, our homes would not be overflowing with disposable junk; in the world where the Luddites won, our wardrobes would not be stuffed full of disposable clothes; perhaps in the world where Socrates won our minds would not be jammed full of nonsense.

One affects memorization and is a trade-off for writing, a process that arguably allows someone to work through their own knowledge of a subject and find or realize gaps in understanding.

Having something else do all of that for you is completely different and essentially tossing any gain outside of the creation of some gray slurry of an output in the trash.