I see from looking around that Aquaman has existed with and fought mermaids and mermen.
Is there any incarnation of Aquaman where he was a merman, was turned into a merman, or had the ability to become a merman?
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One answer is that he is a merman, just not with the appearance you are thinking of. However, I know what you mean.
In the current continuity, they haven't appeared, but in the post crisis world, all the residents of Tritonis (which are the cities near or in Atlantis) appeared as classic mer-people. In the image below you see Iqula, who is the protector of Tritonis.
To distinguish, Aquaman is an Atlantean, and therefore a separate race in the Post-Crisis world (but not in current continuity).
While Atlantis seems to have no shortage of merpeople, Aquaman does not seem to have ever been one of them.
I can find no imagery or references to suggest that Aquaman ever had the telling merman physiology.
Even Superman and Batman have been mermen at one point or another:
But not Arthur Curry.
DC Comics' official profile of Aquaman makes no reference to Aquaman as a merman either.