Can a EU student be an intern in the US ?

In theory, it is possible for an alien to gain a work permit for an internship, it's called the J1 visa. Length issued varies depending on purpose/field, and the application fee is reasonable as well (around 160 dollars? IIRC)

    In order to qualify for a J-1 exchange visitor visa, you need to be coming to the U.S. as a student, scholar, trainee, intern, au pair, teacher, professor, research assistant, medical graduate, or international visitor.   Do I need a sponsor? Yes. The State Department designates U.S. government, academic and private sector entities to conduct educational and cultural exchange programs. To participate in the Exchange Visitor Program, foreign nationals must be sponsored by one of the State Department-designated sponsors.   Who is eligible to be a J1 visa sponsor. The Secretary of State appoints sponsor organizations for J1 visas. These organizations can come in various forms, including government agencies, educational institutions, academic organizations, cultural organizations, non-profit organizations, and for-profit organizations     The company you would want to work for needs to become a sponsoring agency themselves or you could reach out to various existing agencies in the US. I don't think it is difficult to get approved as a company. But I am not sure how difficult it would be to even land an interview with a firm in the first place.   Alternatives: 1) Ask your local banks if they have rotational internships (first in your home country, then US)
2) Ask your local firms or EU firms to refer you to the right contact in the US.
3) Find an agency/umbrella which arranges these kind of internships in the US. There is quite a few of them. Please be aware that some of these charge you a fee, be very careful that these are genuine agencies and not scammers. Other good places to ask for this: your chamber of commerce to get introductions, your own university/their business affairs dept, or also business networks like Rotary Club.   If you simply apply for internships on US career websites there is a risk the relevant colleagues/HR will simply ignore you. They may not know about this visa or that the process looks like.