If you by any chance mean Objective-C, then this might help:
https://developer.apple.com/library/ios/documentation/Swift/Conceptual/BuildingCocoaApps/MixandMatch.html#//apple_ref/doc/uid/TP40014216-CH10-ID122
I haven't played with it myself yet, so I'm not sure if any Objective-C code can call Swift. If that is the case, then any C code in your project can call your Swift code, because any C code is valid Objective-C (i.e. Objective-C is a superset of C). The reverse is not true, however.
Another approach is to have a C function that returns a string that you want to append to the Swift string array. The C function is called from Swift code, which gets the string and actually appends it to the Swift array. You would use a bridging header to make the C function visible to Swift.
A variation of this approach would be to declare a callback function in your C code, import the declaration into Swift using a bridging header, and implement the callback in Swift. This is a more difficult approach, but would come in handy if this part of the app logic is controlled from the C code.
If you provide a more detailed context of what you are doing, people might give you more specific advice or even some examples.