There are 230 4-letter words starting with C in the ENABLE dictionary — 6% of all 3,903 words at this length. C is a one-point tile, so the value in this list is positional rather than numerical — which of these you can play depends far more on where it fits the board than on what it scores.
The list divides into 11 groups by second letter, the largest being the 68 words with co. Scanning the right group is faster than reading the whole list, which is why it is broken up below rather than run alphabetically.
If you know more than one letter, this page stops being the fast way to find it. Enter what you have in the unscrambler — the Contains, Starts with and Ends with filters combine, and setting both length fields to 4 narrows this list to the handful your letters actually allow.
All 230 words, by second letter
CA… (51)
cabs caca cade cadi cads cafe caff cage cagy caid cain cake caky calf calk call calm calo calx came camp cams cane cans cant cape caph capo caps carb card care cark carl carn carp carr cars cart casa case cash cask cast cate cats caul cave cavy caws cays