I think this is a pretty good site, it's general but will work for C code just as for everything else I think!

http://smallseotools.com/plagiarism-checker/

You'll find more by looking for "plagiat checkers" in google

There are many general sites such as:

http://smallseotools.com/plagiarism-checker/

Sure, they will flag everything that "has to be copied" such as int main but everything that "has to be copied" should be common between your students. It should then be fairly easy to not take it into account using a simple script removing anything shared by more than 80% of your students, preferably before submitting it to the plagiarism checker.

It would probably be easier using a website with an API such as: https://api.plagscan.com/guide