Most likely, yes, a business credit card can affect your personal credit score. In addition to your personal credit being used in order to evaluate whether you should get a card, the activity on the business card will be reported to the three credit bureaus and will impact your personal score. As a result, your payment history for your business card can make your personal score go up or down. Also, when you apply for the card, the credit bureaus will consider it a new inquiry, which can lower your personal credit score.
Once your business has been around a while and had the chance to establish a credit score of its own, your personal credit will be less at risk.
Personal Credit Score Vs. Business Credit Score
A personal credit score is linked to your Social Security number, while your business credit score is linked to your Employer Identification Number or Tax ID Number. Also, your personal credit activity is summarized as a numerical score from 300-850, which is calculated by the three major credit bureaus  Equifax, Experian and TransUnion. Business credit activity, however, is summarized in a score on a scale of zero to 100, and is tracked by companies such as Dun & Bradstreet, Experian Business and Equifax Small Business.
Additionally, business credit scores, unlike personal scores, are available to the public though you may need to pay a fee to see it.
Just like with personal credit, it takes time to build a good business credit score, though the process is similar. Maintain responsible financial habits for your business and let time work for you. The age of your business, the type of debt you have and you assets and revenue will all contribute to your score. With business credit scores, factors such as industry risk and any legal filings will also impact it.