Yes. Since a 2011 Rhode Island Supreme Court ruling (Chambers v. Ormiston), the state recognizes same-sex marriages, civil unions, and registered domestic partnerships legally performed in other jurisdictions—including California's domestic partnerships—under the principle of equal protection.
This means California registered domestic partners receive the same state-level rights and obligations as married couples in Rhode Island (e.g., healthcare decisions, inheritance, family leave). Federal recognition depends on whether the partnership is treated as a marriage for federal purposes.