Tere ar
There are quite a few usages, the only ones I can think that are chicken related are cock-a-hoop, which is crowing about something. and cock-fight - pretty obvious what that is.
You could also have:
half-cock - not ready
on the cock - twisted, not aligned (also as cock-eyed)
cock-up - snafu
cock or stop-cock - a faucet or valve
cock and bull story - BS
cockboat - small ship's boat
cockpit - I'm guessing derived from site of cockfighting
cocktail - OED says "unknown origin"
cocky - conceited or saucy
and I'm sure there must be more