If I have a PhD degree from other English speaking countries like India/Singapore/Australia, can I apply for a faculty position in the US?
Yes, you can apply, there is no requirement to have a PhD from any particular country/countries in the US.
At a research university, you'll be judged primarily on your research record. Tenure track positions are extremely competitive, you can be well qualified and have a great record and not get a job even if you apply for many open positions; you need to be supremely qualified and have an excellent record and also be a good fit for the hiring institution.
It varies a bit by field, but many positions will expect applicants to have postdoctoral research experience, as well.