They ARE citizens...

"On March 2, 1917, Wilson signed the Jones-Shafroth Act, under which Puerto Rico became a U.S. territory and Puerto Ricans were granted statutory citizenship, meaning that citizenship was granted by an act of Congress and not by the Constitution (thus it was not guaranteed by the Constitution)."

"Residents of Guam, Puerto Rico and the Virgin Islands are U.S. citizens. ... They are not automatically U.S. citizens; instead they are U.S. nationals, meaning they are entitled to the protection of the U.S. Government but do not enjoy all of the rights of citizenship.May 28, 2008"

"Residents of Puerto Rico and other U.S. territories do not have voting representation in the United States Congress, and are not entitled to electoral votes for President. ... Like other territories, Puerto Rico can participate in the presidential primary process."

" Rights and Restrictions

Restrictions
U.S. nationals cannot vote in any election or hold elected office.

Rights

Allowed to work and reside anywhere in the U.S. without restrictions.
Eligible to apply for U.S. passport just like U.S. citizens. In fact, there is no difference between the passport for U.S. national and U.S. citizen. Both of them mention the 'Nationality - USA'.
Eligible to apply for U.S. citizenship through naturalization under the same rules as other permanent residents. "