There's a couple avenues you can pursue at this point (specifics at bottom). I'll keep in mind the (pretty universal) budget constraints. (note some suggestions are only viable for those with non-tapastic mirrors)
Make sure you're on any and all popular comics listing and consider posting voting rewards for ranked lists: topwebcomics (down at the moment), comicrocket, thewebcomiclist, piperka (more of an aggregator really), and inkoutbreak if it ever comes back up (also an aggregator), so people looking for webcomics can find you. Consider sinking some effort into the community at one or a couple of these to get yourself in front of a larger audience.
Consider listing on more niche sites like the belfry webcomics index. Each of these hosts it's own community and requires a slightly different approach if you want people to notice you, but just being on the site will make it possible.
If you have more time start looking high profile site mirrors: inkblazers (currently breaks in firefox), and tapastic (currently the king, which you are on) are probably the only ones currently worth it. Smackjeeves, comicfury and others I am not currently thinking of seem to be falling by the wayside. Webcomicsnation is gone and keenspace is probably irrelevant.
And/or consider entering a thriving webcomic collective: Hiveworks is slamming. Cup of comics seems to be doing ok. Spiderforest seems to be chugging along with some solid fresh blood. Each has its own set of rules, but a group of like minded comickers and mutual aid/linkage can be quite a force for mutual aid (though tapastic kinda does a lot of this).
You will want to post to social media. It's one of the best ways to reach a wider audience without a hefty financial cost. All of the content marketing rules in the above post apply to social media. Each has it's own ideal post density (rate and post size) and requires consistant updates. Tumblr, twitter, and facebook all tend to be very effective means of promoting a webcomic, but I'd suggest starting with just one and building from there.
There is a very useful site called iftt.com (if this then that) that can automate social media posts (among other things) with each comic update, that and (free) post scheduling sites like Hootsuite can reduce much of the overhead required especially for multiple accounts.
In addition finding and talking with webcomic reviewers and bloggers who might be interested in doing a post on your comic is never a bad idea. I'm personally aware of webcomic overlook, but there's quite a few who might be interested in taking a look at your work if you approach them.
Paid ads are possible too, but I'm afraid it's pretty dependent on your financial situation and goals for the comic (and a large enough subject for another post).
So in your specific case I'd recommend adding your site to any webcomic listings. Then in roughly this order: if you have manpower start one social media account that posts whenever you have an update and includes random making of and anecdotes (perhaps a facebook fan page? They've been doing strange things with fan notifications recently otherwise I'd solidly recommend that initially, tumblr is a solid second). If you have time, consider whether finding a webcomic community fits your goals for the wordpress site and look at those you'd be interested in joining (pros/cons). If you have more time than that consider checking out blogs that might be willing to share your work with their audience and look at creating extras like donation bait (or patreon rewards) for people who want to vote/give you monies. You already have a mirror, so that shouldn't be a high priority, but if you want, look at using IFTT to multiply your social media efforts (it can be set to automatically make social media posts when a new comic goes up, etc).