I did a quick research. Apparently yes you can work remotely for a US company,
and you don't need a visa and not even to pay taxes.
Other sources mention that you would work as a contractor and would need to send invoices as a company.
Obviously you will
- Not benefit from any US benefits such as employment protection, social security, etc.
- Reside abroad and do all your work from abroad.
It means that, in practice, the nature of the work very close to contracting.
If you are interested, maybe check out upwork.com, it looks like an easy start.
On job boards (indeed, monster, etc.) Many of the advertised "remote jobs" require applicants to be based in US or Canada. Others don't mention anything, so I guess it's worth asking.