Can I program the accelerator in C language using High level synthesis compiler ?
That is indeed the main point of the HLS compiler. You can find the documentation here:
Sorry, I thought you meant C/C++ vs. other languages rather than C vs. C++. Either way, the "Intel High Level Synthesis Compiler Reference Manual, Section 3.1" says a subset of C99 and C++ are supported. However, the focus seems to be on C++.