C++ is designed with C compatibility in mind, so it is definitely OK to use libraries written in C from a program written in C++. The language even provides a syntax for using C headers with C++, so what you are trying to do is definitely possible.
In some cases, it may not be ideal from the readability standpoint, because C code may be using opaque handles to emulate objects: this is idiomatic to C, but not to C++. However, this issue can be easily adressed by writing a C++ wrapper around the C library, with very little overhead.