Can I apply for a green card if my parents brought me to the US without papers when I was ten years old?

Significantly more information is needed in order to provide a legal analysis of how your U.S. citizen husband may be able to sponsor you for immigration benefits. This includes, for example, information about the date you entered the U.S., what immigration-related applications, if any, every before have been filed by or for you, etc. There really is no substitute for you and your husband to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.

You can apply, but there are a few things to consider, such as presence, criminal history, entries, etc. You may need a waiver.