No. Nothing in the play shows Desdemona betraying Othello: the betrayal exists only in Iago's insinuations and in Othello's imagination, and each of the "proofs" falls.
The dream that Iago attributes to Cassio is told only by him, who soon afterward says: "No, that was only your dream." The handkerchief that Iago says he saw with Cassio, and that Othello recognizes in Bianca's hands, was found by Emilia on the floor and given to Iago, who threw it into Cassio's room; Emilia says, in Act V, Scene 2: "Did she give it to Cassio? No. I found it." And Cassio tells that Iago confessed to having put the handkerchief there on purpose.
The conversation that Othello takes for a confession, in Act IV, Scene 1, is that of Cassio laughing while speaking of Bianca, and it was Iago who staged it, by saying that he would ask Cassio about Bianca. Othello, hidden, attributes to Desdemona what Cassio says of Bianca.
Those who know the truth say that Desdemona was innocent. Emilia calls the accusation "a horrid lie", Cassio tells Othello: "Dear general, I never gave you cause", and Othello answers that he believes it and asks forgiveness. Desdemona denies it to her last breath, and the letters found in Roderigo's pocket clarify Iago's plot.