I didn't know it was oral cancer awareness month, but my dentist asks me if I want a "screening" for oral cancer every time I go. Seriously, I thought it was just another way for them to make money...
I did some of my own research just now, and briefly (you should check on your own, I'm not a doctor) if you are concerned about oral cancer, you can ask your primary to do an oral exam during your annual physical, or you can ask your dentist for a normal, oral exam (they might even do this normally, but just not tell you?). They'll simply check your mouth and tongue for red or white spots that you would normally not be able to see by yourself. Also, if you have a mouth sore that won't heal, or that lasts for more than 2 weeks, you should get it checked by your doctor.
I haven't really found any evidence for getting the special light test/screening that the dentist keeps asking about (and of course it's not covered by our insurance, so I likely won't be getting it anytime soon), UNLESS you have higher risk factors, which include but are not limited to: tobacco use (of any kind), excessive alcohol use, or previous history of cancer (especially another oral or possibly head/neck cancer).