Source? This quote appears in many places online, but never with any source, besides "attributed to Plato", or "as Plato once said" etc. Usually this means it's not something Plato said. The internet is full of fake Plato quotes.

I got to the 6th page of google results before seeing anything like a source, and followed that trail - "Leadership Manipulation and Ethics in Storytelling" by T Auvinen, 2013, cited 110 times, says "Even Plato stated that those who tell stories rule society (Fisher, 1985)". So I looked at that paper, WR Fisher's "The Narrative Paradigm: In the Beginning" (1985), which doesn't contain that quote or anything like it! It does say, in its one paragraph about Plato:

"[Plato's] “contribution” to the transformation of logos was to technologize it, to make it a term appropriate to only philosophical discourse. The effects of his thought were to create “experts” in truth, knowledge, and reality; to establish the rational superiority of philosophical (technical) discourse; to relegate mythos to myth (meaning fictional); and to downgrade rhetoric and poetic. Dispensations were made for rhetoric and poetic; they had a place in the life of the community but they were not to be considered serious intellectual arts. They were to be controlled or informed by philosopher-kings."

Which is vaguely is in the right ballpark - although more like its opposite. Tentative conclusion: Plato didn't say that.