ASNT issues a card if you pass their ACCP level II or III exam(s) or their ASNT NDT Level III exam(s). In order to do that, you have to apply and be approved by them to take said exam(s).
It is the employers responsibility to certify NDT personnel, or to ensure that NDT personnel from an outside agency meet their requirements.
If you have zero UT experience, and you are not doing UT as part of your job, you will have a hard time getting the required experience to make it to level II. Do you have an NDT program at your employer now? The reason I ask is because you stated that "we have a need for that where I currently work" If there are no UT level II or III where you currently work, and no written practice, well....
As far as home study goes, section 7 of SNT-TC-1A recommends "sufficient organized training to become thoroughly familiar with the principles and practices of the specific NDT method"....etc. If your employers written practice follows this recommendation, you will not meet te requirement with home study.
For what it's worth, our written practice requires documented proof of training, and requires that the training include sufficient examinations to demonstrate that the necessary information has been comprehended.