The Verdict: Unlikely
Croatian law gives you residence as a life partner but not the spouse's citizenship shortcut. Plan on residence and ordinary naturalisation, and check any Croatian roots of your own first.
The Aliens Act treats the life partner (životni partner, registered or informal) of a Croatian citizen like a spouse for residence. Article 70 gives temporary residence, and article 156(1)(1) gives permanent residence after four years.
The Citizenship Act was never amended to match. Article 10 says brak, marriage, and Croatia has no same-sex marriage; a same-sex marriage concluded abroad is treated as a life partnership. That gap is the law as it stands, not anything about your case.
What remains is ordinary naturalisation under article 8: eight years of registered residence with permanent residence, Croatian at B1 with the culture test, and release from your current citizenship. Our Naturalization quiz sets out each step. The descent and diaspora routes ask nothing about your relationship, so check those first if you have Croatian roots.