Some of these pictures and descriptions may give away plot details that you might not want to know before watching the film.
This is a epic about Jewish gangsters in New York City from the master of the Spaghetti Western, Sergio Leone, with a great musical score by Ennio Morricone.
The snake scene appears in the Extended Director's Cut of the movie, which is over four hours long, but better than the edited version. It appears to be one of the scenes cut from the original version since it has not been color corrected (or maybe it was intended to look that way.)
Deborah (Elizabeth McGovern) is a childhood friend of the protagonist Noodles (Robert De Niro) in the 1920s. After he raped her the night before she left New York to go to L.A. to become an actress, they became estranged. (There's no way she would dare go to the police to accuse a powerful gangster who is paying them off.) In the late 1960s she meets with Noodles again. He goes to a theater to see her perform Shakespeare's "Cleopatra." We see her on stage acting out part of the suicide scene where Cleopatra pulls a venomous snake out of a fig basket and makes it bite her breast to kill herself. Just to make sure she gets a fatal dose of venom, she makes a second snake bite her on the arm. The second snake is in the original play but it's not usually seen in movies. Shakespeare was no dummy - he takes no chances with low venom yields or dry bites, and you have to respect him for that.
The snake used in the scene appears to be a non-venomous garter snake or ribbon snake.