Of course you can. The best tool for the job is a pneumatic stapler
or even a manual heavy duty one, or failing that, some small nails, or as a last resort, glue (epoxy maybe) The thing is--is that frame you have 1/2" wide moulding? Or 1/2" tall? If you have at least 3/8" under the lip inside the frame, it will hide the edge of your board. Buddy ,I was custom picture framer for 12 years, I can tell you anything about this stuff, but it's still hard without seeing what your trying to fit. I can tell you that a 1/2" frame is ridiculously small for (any use)is it a cheap diploma frame ? What is are the dimensions of your board? Is it really the size you want? Can you maybe find/buy a better frame? can you post images of what your working with?