I am currently a visiting assistant professor in Computer Science in the United States. I was wondering If there are any avenues (ARC programs) for someone like me to apply for research grants in Australia.
This depends on your personal circumstances.
As others have suggested fellowships like the DECRA if you're within ~ 5 years of your PhD or Future Fellowship if you're further along in your career (though note that Australian candidates take preference in FFs). A Discovery International Award (or other Discovery-Family award) could also fit the bill, details for all of these are on the ARC site linked by others.
If you're willing to look beyond ARC funding many Australian universities also have their own schemes to attract outstanding international scholars for short or long-term positions or exchange programmes with international unis.
Assuming you are willing to move to Australia, you could apply for one of the ARC fellowships. You would need to find a host institution. If your doctorate was awarded recently, DECRA would the best program for you.