This thread on User Experience Stack Exchange discusses the choice of key bindings C for copy makes a lot of sense. I don't know exactly when that was, but it must have been the late 1970s. The “copy” meaning of Ctrl+ C comes from Xerox PARC, the inventors of copy-paste in its modern form (and most other fundamentals of graphical user interfaces). Lacking a character meaning “stop”¹, a character meaning “this segment of input is over” was a reasonable choice to mean “stop the current processing”. The article explains why Ctrl+ C was a reasonable choice: in ASCII, which was published in 1963, the corresponding character is ETX, end-of-text.
Wikipedia traces it back to TOPS-10, which would date it from the late 1960s.
The “kill” meaning of Ctrl+ C is very old, I think even older than Unix.