Currently, you can invest up to USD 250,000 every year in foreign stocks from India. This amount can change, subject to RBI guidelines. So your investments in US securities are also governed by the same limit.
Foreign investments fall under clearly defined RBI guidelines. The remittance of money for foreign investments comes under the Liberalized Remittance Scheme (LRS). Under LRS an Individual can remit up to USD 250,000 per financial year to invest in foreign equities done through an authorized dealer (commonly, your bank). As per the RBI policy, having a PAN card is required to purchase shares in foreign countries. You can find more information on the LRS scheme on the RBI website here.
Disclaimer: This article is for informational purposes only. None of the contents of this article should be treated as tax advice. Please consult a qualified tax consultant or expert with your specific taxation situation for appropriate advice.