The Capistrano 3 guide recommends the use of passwordless sudo. This allows your less-priveleged user execute the sudo command without having to enter a password via the PTY.
You can use the task that Kentaro wrote above, and add something like the following to your /etc/sudoers file:
deploy ALL=NOPASSWD:/bin/cp ~/something /something
http://www.capistranorb.com/documentation/getting-started/authentication-and-authorisation/#toc_8