Yes, if the 7 tests below are met. There is no rule against "taking turns." The only rules that matter are these ones:
1) You provided more than half
of their financial support. More info
2) They made less than $4,050 in gross income
during 2016 unless they are a
qualifying child (under 19 OR a full time student under 24
OR permanently disabled)
3) They live with you or they are related to
you.
4) They are a U.S. citizen, resident alien,
national, or a Canadian or Mexican resident.
5) They aren't (or won't be) claimed as a
dependent by someone else.
6) They aren’t filing a joint return with
their spouse.
7) You are not being claimed as a dependent on
someone else's return.
If you do claim him as a dependent, he will
still need to file his own return and he should answer Yes to "can someone else claim you as
a dependent?"