You'll have to apply for a visa - it can be done online if certain requirements are met. Otherwise, you may have to visit the embassy or one of the consulates of Sweden in the USA. They should also be able to answer questions authoritatively.
Usually, you have to be able to prove your residency in the country where you apply the visa (in the US for your case).
Since you are a student, then it should be easy for you since you have a Student Visa / Resident card.
But as always, the safer is to just ask the concerned embassy.