You don't really need all the infrastructure in a full compiler like LLVM
for it either, regular expressions are rather simple.
One old style version (non JIT) is re2c that simply compiles regexprs to C.
Then the V8 java script engine in google chrome which uses an own compiler for their JS regexprs. Undoubtedly there are others too. e.g. in a language with built in compiler like Common Lisp it's rather easy to do.