Possibly.
It depends on whether there's an organization that actually coordinates "exchanges" (in other words, they're also helping to arrange placements for US students abroad). Most of those don't pay.
But there are lots of families providing "homestays" for foreign students. Usually the organizations recruiting families to provide homestays work only with international students who want to study in the US (in other words, they're not placing US students in other countries). Quite often, these families are paid for hosting - not tons of money, but certainly enough to cover the added expenses.
Technically, the students living with US families on "homestays" aren't exchange students, but because most people don't really care about the technicalities, any international student often gets called a "foreign exchange student."