As a player, Rubini won a silver medal with the senior Italian national basketball team, at the EuroBasket 1946, held in Geneva. Later, as the delegation head of the senior Italian national basketball team, Rubini also took part in the first international victories of Italy: these include the silver medal at the 1980 Summer Olympic Games. At the EuroBasket, Italy finished first at the 1983 EuroBasket, in Nantes, finished third at the 1985 EuroBasket, in Stuttgart, and finished second at the 1991 EuroBasket, in Rome.