That's going to be an uphill battle. You are competing with people of your age have significant real word experience. Let's dissect this a bit
I am a Ph.D. student.
No plans to finish your Ph.D.? What do you have to show for it?
I have been involved with academia for some time now.
How long? One year, 3 years, 5 years? This makes a huge difference.
For some reason, I need a job in the industry
That better be a really good reason. It looks like you are abandoning all the time and effort you spent on your Ph.D. That will require some serious explanation.
but my CV is not garnering any interest in the industry.
Given the analysis above, that's not particularly surprising.
How can I showcase my expertise to potential recruiters if I don't have enough job experience?
It's hard to showcase expertise you don't have. I'm guessing your biggest problem is lack of industry skills that many of your competitors will already have. These are mostly "soft" skills: work management & breakdown, communication & documentation, working effectively in multi-faceted teams, organizational awareness, business focus, etc. All of these tend to work very differently in industry than in academia.
What you can do:
- Network, network, network. Join professional associations and attend their meetings. Go to conferences: present your stuff and attend presentations from industry people who work in similar fields. Try to make a name for yourself that you are good at XXX, whatever that may be. Hang out on Stack Exchange and other internet forums of your "people".
- Have you resume critically reviewed by an expert or experienced recruiter. Make sure you have a strong story that supports you abandoning your Ph.D.
- Consider finishing your Ph.D. if you are reasonably close to the finish line. That would look A LOT better on your resume.
- See if you can get some amount of industry experience as an intern, temp, free-lancer, etc.