This is a good question. There are two places in the book when Atticus speaks of the death penalty. From these two contexts, it is possible to say that Atticus is not against the death penalty. However, he would want the death penalty to be granted only by a judge and not a jury. In other words, he does not think it is wise to grant a jury the power to grant the death penalty, because people are racist. He writes:
“Given,” said Atticus. “Tom Robinson’s a colored man, Jem. No jury in this part of the world’s going to say, ‘We think you’re guilty, but not very,’ on a charge like that. It was either a straight acquittal or nothing.”
Atticus, then, explains his point further:
Atticus dropped his newspaper beside his chair. He said he didn’t have any quarrel with the rape statute, none what ever, but he did have deep misgivings when the state asked for and the jury gave a death penalty on purely circumstantial evidence.
In the case of Tom Robinson, Atticus know that the trial was a farce. Racism won out in the end. That said, Atticus did not lose hope. He was going to appeal and he believed that he a good start in getting Tom acquitted.
Atticus does not seem to be against the death penalty, however, he feels that juries should have clear proof of evidence. He feels that a jury's decision should not be based on circumstantial evidence. Atticus does not believe that it should be so easy to grant someone the death penalty. He feels that, the more witnesses there are to crime, the more valid an jury's decision is.