Can you get a credit card being on unemployment insurance?

Yes. Employment is a factor in the ability to pay. When you are scored your employment status is a factor but doesn't prohibit you getting a card. Plently of people what are independently wealthy (e.g. their income is the results of investment rather then employment) get credit cards all the time. The key is the ability to pay and the risk of non-payment. If you are broke and have no job and no income you will likely be declined.