Frank Sinatra was an American pop figure, he rose to fame in the 1950s and is considered an influential celebrity of the 20th century. Rockstar intentionally referenced Frank, to highlight his criminal controversies, most notably with the Mafia. Frank Sinatra's portrait can be found at Marco's Bistro.
Vice City Mafia
Frank Sinatra had controversial ties with the Italian-American Mafia. Willie Moretti, mafia lord, helped him get breakthroughs throughout a particular phase of his career. Sinatra is also known to have attended the Havana Mafia conference in the year 1946. He had strong ties with the infamous mafia lord, known as Lucky Luciano. He was allegedly the best friend of the American mafia lord, Sam Giancana. His controversial and professional links with the mafia is regarded as a subject of contention for him.
It is highly likely that Rockstar placed his portrait at Marco's Bistro, to reference Vice City Mafia and supposedly his tendentious links. Players have speculated that he is related to the Forelli Family and their infamous mafia nexus.