If you want to execute something like "pop %[register] push %[register]" as you write in your comment, yes, this is possible, but it isn't easy.
You need to either write an assembler or embed an open source assembler in your application. You feed your assembler with your char array, create the machine code (preferably PIC code, so you can omit the linking and relocating) in an other buffer and execute code in this buffer via a function pointer.
If you can guarantee there is an "as" or "gas" on the platform you run the code, you might get away with a quick and dirty hack to call "as" with your code piped in and the object code piped out.