Frank Sinatra was an American actor, singer, and producer. A former member of the Rat Pack, he is hailed as an icon of the entertainment industry.
Reuben Tishkoff and Willy Bank have both met Sinatra at some point in their respective pasts. Both Reuben and Danny mention to Bank that anyone who shook Sinatra's hand is considered worthy of knowing a code among those who have done it. The implication being that this group of individuals are respectful and ethical, especially or very likely, to one another.