The country, with around 34,000 citizens, has yet to start its vaccination campaign.
To date, it has reported around 3,400 coronavirus cases and 72 deaths.
Before turning to Russia it had agreed a vaccines deal with Italy, but this has been undermined by the supply shortages faced in many European countries.
“The fight against coronavirus must not have any geopolitical connotations and must know no borders,” Foreign Minister Luca Beccari said in a statement.
“Small European states like San Marino must be able to ensure a uniform vaccination campaign across their territory,” he added.
San Marino authorities said they expected to start administering the first doses of the vaccine “in the coming days”.
The Russian vaccine has not been authorised by European Union authorities, but since San Marino is not a member of the bloc, it is not bound by its rules.