Maxim Lapunov was arrested by police officers and beaten up while living in Grozny, Chechnya’s capital, in 2017.
More than 100 gay men are believed to have been rounded up and tortured in Chechnya during 2017, according to rights groups.
Local authorities have denied that the crackdown ever happened, despite reports to the contrary in local media.
Mr Lapunov was the only man who lodged an official complaint with the police following the alleged violence.
The Russian citizen was living in Chechnya, an autonomous, mainly Muslim region of Russia, at the time of his arrest.
Despite his criminal complaint, a North Caucasus court ruled in 2018 against opening a criminal investigation into the case.
Justice minister Alexander Konovalov said a preliminary probe into the reports found no evidence of arrests and torture.
But in December last year, the Organisation for Security and Cooperation in Europe said the allegations were “credible” and “confirmed”.
The regional security organisation urged Russia to conduct a full investigation.
Mr Lapunov’s lawyers said on Friday that they had approached the ECHR after exhausting all available legal options in Russia.
Their client is now seeking compensation from the Russian government, for failing to protect him from torture, discrimination and unlawful detention.
“For two years, Maxim Lapunov, who claimed to have been tortured in Chechnya, did not achieve an effective investigation of his complaint at the national level,” the Committee Against Torture, a Russian NGO, said in a statement.
The human rights group is representing him in the proceedings.
“Now the Strasbourg judges will have to give their assessment of both the fact of unlawful detention and torture against the applicant, and the actions of the investigators.”
Earlier this month the US imposed sanctions on a Chechen group over allegations of human rights abuses, including of the torture of LGBT+ people.
Human rights groups have also warned that a new wave of anti-LGBT+ violence is emerging in Chechnya.
Human Rights Watch said it interviewed four gay men who claimed they fled the conservative, predominantly Muslim region after police allegedly beat and shocked them with electric currents while they were strung up by their legs.
The men were allegedly detained between December 2018 and February 2019.
Additional reporting by agencies