Can you put auto insurance on your drivers license?

The question isn't fully clear. A license is needed to operate a vehicle. Driving skill is needed to get a license as there is generally a written test plus one to test actual driving ability.

It is often required that the drivers license applicant produce proof of insurance that complies with the state's financial responsibility laws. If the applicant owns a vehicle, it must be insured according to the state's requirements, and that proof of insurance must be shown

If the applicant does not own a car, he/she may obtain "non-owners coverage". It generally satisfies the requirements of state financial responsibility laws. In that sense, I suppose, you are "putting auto insurance on your drivers license".