Can you apply for a CDL if you have a DWI?

Not as long as the resulting suspension period from your DUI conviction is in effect. If it has passed, and you've reinstated your licence, you can upgrade it to a CDL. If your DUI occurred within the past 10 years, your prospects of finding employment as a CDL driver are slim. If it's been within the past five years, you'd be best advised to pursue another career path, and not waste your money getting a CDL.