It is Cassius more than Casca who wants Brutus to participate in the conspiracy to kill Caesar. Furthermore, in Act 1 Scene 3, Cassius reveals that his real motive in wanting to murder Caesar is that he doesn’t like the man. He tells Casca “why should Caesar be a tyrant, then? / Poor man, I know he would not be a wolf / But that he sees the Romans are but sheep….What trash is Rome, / What rubbish…when it serves / For the base matter to illuminate / So vile a thing as Caesar” (106-115). Cassius knows he lacks moral grounding in killing Caesar, and he thinks less of Casca than he does Caesar, calling him “dull” and otherwise insulting him in the same scene (60-70). Casca is such a coward that he is unnerved by the storm then raging. Lacking moral grounding, Cassius seduces Brutus, who has moral standing among the Senators as well as among the people, to join the conspiracy, convincing him that Caesar is ambitious and will undermine the Republic. Casca is more of a "yes man" to Cassius, doing as he is told or as he expects Cassius wants him to do--he has little to do with persuading Brutus.
They have to get Brutus to join them. Brutus is extremely well-loved by the people, and his participation will make their actions more acceptable to the rest of Rome.