Yes, if you believe the mirror test proves it:
The bluestreak cleaner wrasse has passed the famous mirror test for self-recognition (originally intended for primate apes and monkeys).
According to a recent paper (open access), three out of four fish tested by researchers from Osaka City University in Japan were able to learn to identify the object in a mirror as their own images. But what does that mean?
When chimpanzees, dolphins, elephants, and magpies passed the test1, researchers theorized that these animals, recognized as intelligent, were demonstrating a concept of “self.” Now they are not so sure. Is the cleaner wrasse, which grooms other fish for parasites, really self-aware? Are fish much smarter than we think? More.
But what if the whole question is founded on a mistake about the nature of the mirror test?
Overall, it’s a curious outcome for the mirror test. Those who felt reassured by close kinship with chimpanzees reacted quite differently when offered close kinship with fish.
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See also: How is human language different from animal signals? What do we need from language that we cannot get from signals alone? (Michael Egnor)
Why only human beings speak: Language is a tool for abstract thinking—a necessary tool for abstraction—and humans are the only animals who think abstractly. (Michael Egnor)
and
Animal minds: In search of the minimal self