Judging by his final summation to the jury serving in the Tom Robinson trial, Atticus Finch absolutely believes in God. Although he rarely if ever goes to church, Atticus is a God-fearing man with a solid moral base. After stating the facts and the social injustice of even charging Tom with rape, Atticus appeals to the jury's own religious instincts when he asks them
"In the name of God, do your duty."
Atticus's voice had dropped, and as he turned away from the jury, he said something I did not catch. He said it more to himself than to the court. I punched Jem. "What'd he say?"
" 'In the name of God, believe him,' I think that's what he said."
We also get a hint of Atticus's religious upbringing when Scout tells Miss Maudie in Chapter 5 that "Atticus says God's loving folks like you love yourself--."
Yes he does, but it is not written directly in the story. The children go to church and taught about what is right and wrong such as sins.
In the opening of the book "To Kill a Mockingbird" the family ancestry is discussed by Scout. In it she talks about the ancestor Simon being a Methodist. However, he was only happy doing that which was not for the glory of God. Scout goes on to say that Sundays in Maycomb people went to church and visited afterwards. The book does not directly state that Atticus believes in God, but Atticus demonstrates moral behaviors and compassion for others. He lets Calpurnia take the children to her church. I believe that Atticus believed in God, but was not a man who preached the gospel.
I do want to state that people can exhibit moral behaviors and attitudes of compassion and honesty without a belief in God. At the same time there are many people who express a belief in God and don't have compassion or kindness towards others.