As you're discovered, many such summer programs are limited to US citizens and permanent residents; my understanding is that this is due to the source of their funding. Nonetheless, some programs exist which are accessible to international students. Unfortunately, since the funding source is what limits participants to US citizens/permanent residents, international participants might have to forgo funding, or pay. Here are the few programs I know of:
Undergraduates funded by PCMI may receive lodging, travel, meals and a
stipend (stipends are awarded to U.S. Citizens or U.S. permanent
Applicants to the program should be women who: 1) are applying to PhD
programs in the mathematical sciences, or 2) just completed their
first year in a PhD program in the mathematical sciences.
Women from underrepresented minority groups are especially encouraged
to apply. Final acceptance to the program is contingent upon
enrollment in a PhD program in Fall 2015. Unfortunately, at this time
we are only able to fund US citizens and permanent residents.
U.S. citizens or permanent residents who are selected into the
program, will receive a stipend of $3,600, housing in the university
dormitories, and allowances for food and travel.
Non U.S. citizens or non residents who are selected into the program,
will be expected to pay a registration fee of 4,000. In addition,
they are responsible for their own housing, travel and food.
University housing will be available for approximately $2,000 for the
duration of the Institute.
In addition, as mentioned in the comments (to the question) by James Cook, there might be sources of internal funding. If you are currently enrolled in a university, it is probably worthwhile to ask faculty members there.