The C language is not a piece of software but a defined standard, so one wouldn’t say that it’s open-source, but rather that it’s an open standard.
There are a gazillion different compilers for C however, and many of those are indeed open-source. The most notable example is GCC’s C compiler, which is all under the GNU General Public License (GPL), an open-source license.
There are more options. Watcom is open-source, for instance. There is no shortage of open-source C compilers, but without a doubt the most widespread one, at least in the non-Windows world, is GCC.