Of course you can

Theoretically you can apply through PERM as Research Associate, but you won't get any information from here, talk to your human rescource/international office to get the regulation of your school for cases like this. I know some schools don't sponsor GC unless you are a faculty whereas other will sponsor it. Even if they don't, ask your boss to pressure on them for your application, say you are important and blah, blah. In addition, consult some experienced immigration attorneys for your case, such as www.murthy.com or www.immigration.com or www.shusterman.com or someone based on friend's recommendations. Good luck.