If you want something lightweight, that runs in the same process as the server, I highly recommend Bull. It has a simple API that allows for a fine grained control over your queues.
If you’re looking for something that runs as a standalone worker process, perhaps look into Kue. It can run as a RESTful API server, and even has several front-end apps written for it.
If you’re familiar with Ruby’s Resque, there is a node implementation called Node-resque
Bull, Kue and Node-resque are all backed by Redis, which is ubiquitous among Node.js worker queues. All 3 would be able to do what RoR’s DelayedJob does, it’s matter of specific features that you want, and your API preferences.