>> Article 14 – Prohibition of discrimination:
>> The enjoyment of the rights and freedoms set forth in this Convention shall be secured without discrimination on any ground such as sex, race, colour, language, religion, political or other opinion, national or social origin, association with a national minority, property, birth or other status. [0]
Granted, its not about marriage, but according to the ECHR, its a human right to live free of discrimination based on sexual orientation.
[0]: https://www.coe.int/en/web/conventions/full-list/-/conventio...
[Edit] There is this, which seems to leave it to the nations:
>>Article 12 – Right to marry
>> Men and women of marriageable age have the right to marry and to found a family, according to the national laws governing the exercise of this right.
ECHR has ruled that relationship of two same-sex partners falls under the notion of "family life". It means equality of treatment and non-discrimination in regard to the protection of family life.
But no same-sex marriage right. I's my understanding that this is difference between individual rights and state obligations.