Probably the best way to do this - assuming that you can't use the NOPASSWD solution provided by scottod - is to use Mircea Vutcovici's solution in combination with Ansible vault Archived.
For example, you might have a playbook something like this:
- hosts: all
vars_files:
- secret
tasks:
- name: Do something as sudo
service: name=nginx state=restarted
sudo: yes
Here we are including a file called secret which will contain our sudo password.
We will use ansible-vault to create an encrypted version of this file:
ansible-vault create secret
This will ask you for a password, then open your default editor to edit the file. You can put your ansible_sudo_pass in here.
e.g.: secret:
ansible_sudo_pass: mysudopassword
Save and exit, now you have an encrypted secret file which Ansible is able to decrypt when you run your playbook. Note: you can edit the file with ansible-vault edit secret (and enter the password that you used when creating the file)
The final piece of the puzzle is to provide Ansible with a --vault-password-file which it will use to decrypt your secret file.
Create a file called vault.txt and in that put the password that you used when creating your secret file. The password should be a string stored as a single line in the file.
From the Ansible Docs:
.. ensure permissions on the file are such that no one else can access your key and do not add your key to source control
Finally: you can now run your playbook with something like
ansible-playbook playbook.yml -u someuser -i hosts --sudo --vault-password-file=vault.txt
The above is assuming the following directory layout:
.
|_ playbook.yml
|_ secret
|_ hosts
|_ vault.txt