No. Puerto Rico doesn't ask visitors to fill in an online arrival form (also called an entry form, immigration card or landing card) before they travel. US territory: US entry rules apply, including ESTA for some nationalities.
Do I still need a visa for Puerto Rico?
An arrival form is not a visa. Whether you need a visa or an electronic travel authorization depends on your nationality, so check Puerto Rico's official immigration website or your own government's travel advice.
Other countries in North America, Central America and the Caribbean