It is definitely not weird… (or uncommon) to have to pay to intern abroad. It may seem strange to have to pay to work, but, it’s not quite as (comparably) simple to arrange as your typical local internship.
If you think about it, it does cost those organizing the international internship time, effort, and money to do so.
By connecting you with a placement across the globe, accommodating your time abroad, and assisting you with your travels, it makes sense that part of what you pay for is paperwork and convenience.
Especially if you are, in fact, utilizing some sort of exchange program, part of the price may even go toward covering permits, rent payments, etc. that would otherwise be coming out of your own pocket anyway.
Not to mention, it saves yourself a lot of the extra work that an international internships requires by tapping into the expertise of those whose job it is to arrange these types of things smoothly and efficiently.