Most banks will certainly ask for your Social Security Number when you apply for a business card. It is called a personal guarantee, which is required by almost every bank for small business cards.
The only exclusions from that requirement are medium to large businesses with more than 2 years in business, substantial assets, and profits (for instance more than $1mm in annual sales and more than $350,000 in annual profits).
Your personal guarantee will make you responsible for any problems with repayment of your business credit. If your business fails or you miss regular payments on your business credit card, not only will your business credit be damaged, but your personal credit will take a hit as well.
If your personal credit is not good enough to have it as a guarantee, you can apply for a secured business card to build your business credit. With a secured credit card, you will still sign a personal guarantee; it will be just easier to get your application approved regardless of your credit score.
no annual fee
low 10.49% APR based on your credit worthiness
12 months 0% intro APR