Unfortunately, no, you cannot claim a foreign exchange student as a dependent on your tax return.
However, if the student was formally placed with you through a government agency or some non-profit organization, then you can claim up to $50
per month as a charitable donation.
For more details, please see IRS Publication 526 (2016), Page 4 here (Topic:
Expenses Paid for Student Living With You)
https://www.irs.gov/pub/irs-pdf/p526.pdfThank you for asking this important question.