Throughout Othello, there are many references to Iago being a devil or villian. Likewise, Christian theology of heaven and hell blankets the text. There is an apparent battle between good and evil that is embodied between God and the devil, who is most easily seen in the character Iago.
I would note that the word Satan is not used. Devil is often used by others, but in a conversation with with Cassio, Iago calls himself a villian in this line:
I am a very villain else.
This line is spoken as Iago is trying to learn if Cassio is going to marry Bianca. Iago uses this line after telling Cassio that there are rumors flying about stating that Cassio and Bianca will marry. Iago says this line meaning if the rumors aren't true, he is the devil himself. This line occurs in Act IV, scene i.
Many characters allude to hell or Iago as a devil or villain. Your question specifically asks where Iago calls himself this being. This is the only spot I can find where he uses the word I, a verb stating existence, and a synonym to your word Satan. Emilia calls him the "eternal villian" in Act IV.ii, line 130. Othello calls him a devil in Act V.
The first two links below will give you many more references.