While this is constantly suggested, no major historian I have read (and these are pretty much THE sources on Indian history - source list below) has actually provided any sort of proof or even vague evidence to suggest this.

While India has had republics 1, we do not know if Kalinga was ever a republic or democracy of any type. Romila Thapar 2 (and other historians) does say that ancient India had a type of a democratic set up called the "Gana Sanghas or Rajya". Where some regions might have had this loose democracy of sorts. A grouping of clans assembled at a particular place, the topic to be discussed was tabled, the group discussed and if a unanimous decision could not be reached, the matter would be put to vote. For some context, Gana means assembly and Rajya means governance, so combined, this would literally mean governance by assembly. D D Kosambi 1 does also say that such republics (not democracies) existed in the kingdoms of Licchavi or Mallas.

Now, was Kalinga a republic? We just don't know, but nothing in the Ashokan rock edicts suggests that this was the case.

*1 - The Culture and Civilisation of Ancient India in Historical Outline by D D Kosambi,

*2 - The Penguin History of Early India by Romila Thapar.

Another clue as to why this might not be true is that the King Kharavela (Ashoka's near contemporary) from Kalinga comes from "King Cheta's Lineage" (as found in some rock edicts), and hence it indicates that even before the take over of Kalinga by Ashoka, Kalinga had kings, and one line survived the battle and the direct successor was Kharavela.