No, you are allowed to travel to Puerto Rico regardless of vaccination status.
If you are unvaccinated, you must provide a negative COVID test (antigen or PCR) from the last 48 hours or within 48 hours upon arrival to Puerto Rico.
Travelers who have tested positive for COVID-19 within 90 days of their entry to Puerto Rico are permitted entry only by presenting a certified medical health certificate from a doctor stating that they have fully recovered from COVID-19, along with proof of the positive test from their previous diagnosis
Upon arrival, all guests of all hotels, Paradores, guesthouses, and short-term rentals across the Island must present either proof of vaccination or a negative PCR or antigen test performed by an authorized health provider taken within 48 hours of the beginning of their visit.
All establishments serving food or drinks must require proof of vaccination or a negative COVID-19 test (either antigen or PCR performed by an authorized health provider) taken 48 hours prior to arrival. Children under 5 are exempt. Please note this does include entrance to the wedding reception at La Concha.