Indeed has a brilliant Affiliate System, based on pay per click method. You can get a JobRoll directly from Indeed, you have just to include some script to your website.
But, if you would like to use more deeply their API, you can get the jobs feed via cURL in XML format.
It is more complicated, so I can recommend you if you have any experience in Web Developing.
Doesn’t enough to get the jobs via the API, you have to integrated well some other files and methods in your website.
Indeed doesn’t allow caching, so take care with the job feed, it isn’t a good idea to save it in the database. If you even do this, you have to delete the expired jobs soon. (maybe few hours caching doesn’t mean any trouble)
Important thing, you have to know, not all of the jobs are sponsored. It mean you won’t get a revenue on every clicks on the job’s links. Some of them sponsored, some of them not. But it is even a great opportunity to monetize our website with some helpful job offer and display some extra content.
If you would like to do it with WordPress you can use the WP Job Hunter Plugin.