Gprof tells me that my computationally heavy program spends most of it's time (36%) hashing using AP-Hash.
I can't reduce the call count but I would still like to make it faster, can I call intrinsic SHA from a c program?
Do I need the intel compiler or can I stick with gcc?
Unless you work at Intel, you can't yet. SHA extensions have not yet been included on any released CPU; they are expected to be included in Intel's Skylake microarchitecture (which isn't expected until 2015 or 2016).
Moreover, the AP hash function is probably already faster than even an accelerated SHA would be. You may want to consider alternative approaches, such as optimizing the hash function or caching the results for hot values.