If you have social security number and you are a student, you can apply for a student credit card without annual fee charge.

Wells Fargo provides such student credit card, I do not know other banks. 

谢谢各位的帮助。但我老公不是学习，而是博士后，J1签证。抱歉没有说清楚，有什么好的选择吗？

www.cardratings.com 上有各种credit card的介绍和推荐。也可以在google上搜一搜。