Currently I'm using the delay method (e.g. my_user.delay.background_task) of delayed_job and it's successfully creating an ActiveRecord entry for the delayed job, but it never runs. How can I make a worker run the delayed_jobs on DigitalOcean using Unicorn?

I guess this will answer your question:

http://stackoverflow.com/questions/14842519/unicorn-rb-heroku-delayed-job-config