Yes, individuals can apply for small business cards even if they do not have a corporation or LLC.
When you apply as an individual, you're applying as a sole proprietor.
When you do that your business name will be the same as your legal name. For example if your name was Wayne Smith, you would also enter that for the business name field on the application.
For your tax ID number, since you are applying as an individual it will be your Social Security number.
The best part about business credit cards is they generally have higher rewards than personal cards. The reasons for this are (a) it costs merchants more to process them, and (b) account holders of these types of cards usually charge more.Check out my article about Ink Plus versus Ink Bold
. In it I talk about applying as an individual.